Training New Fighters

The major advice I'd give is to get trained before you start to fight.
By this, I mean that you should learn how to perform the various techniques of both sword and shield before you have to use them in a full-speed fight.  This training should include plenty of pell and mirror work.  You don't learn a technique just because someone showed you how to do it, and you repeated it, more or less, a few times.
Once you've learned the techniques, integrate them by practicing rhythmic slow work.  Eventually, escalate the speed of the slow work, keeping it rhythmic, until you approach full speed.  When you speed up the slow work, it may be wise to get into armor.
Have someone explain some of the other things that you need to know to be able to fight effectively, like range control, timing, telegraphing, feints, etc.  Practice these in the controlled-speed fighting that follows.
A lot of the things (not the fast-speed practices) mentioned above can be done unarmored.  You don't need to finish your kit before you start doing them.  If I took on a new student who was really serious about learning the art, he/she wouldn't get in armor until they had trained for months.
Then do controlled-speed fighting, which is not rhythmic, and escalate the speed until you are at full speed.
Along the way, include exercises to improve yourself in specific techniques.
Remember that "just fighting" is NOT an effective way to learn the art.  If you were taking up boxing or judo, you would do a lot of work on learning individual techniques and integrating them, then learning how to use them at full speed, before you got into an actual match.
Exercise some common sense.  If someone tells you to use a technique that doesn't make sense, or which hurts you to use, ask them to explain why it makes sense, and what you can do to keep it from injuring you when you use it.  Saying "Yes, but....." is infuriating to teachers.  Asking for explanations and elaborations is not.  If necessary, you can always check with me, either on the forum, or by private post.
Remember that you only have so much strength, speed, and agility.  You can improve yourself in each of these, and you should attempt to do so, but it is only possible to do so to a point.  You can learn technique and perception, and there is no limit to how far you can progress in these areas.
Do not neglect conditioning.  No matter how good you get, you can't win fights if you're too tired to swing a sword, or to block your opponent's blows.

Choices for the New Fighter

I am very much in favor of teaching the basic techniques of sword and shield before moving to the other weapons.  A lot of what goes into fighting, with whatever weapon form is used, can be learned with sword and shield.  Moreover, it is usually easier to teach these aspects of fighting - power generation, balance, movement, rhythm, perception, etc. - with sword and shield.
I feel that this is true, even if the aspiring fighter's interest is purely in war fighting, rather then tournaments.
However, people should get to make their own choices.  If someone is determined to fight only with great weapon or spear, then that is his or her choice.  If it means that it will likely be more difficult to realize their potential as a fighter that is also their choice.  I don't force anybody to do things my way. 
I am reminded of an old saying; "Never attempt to teach a pig to sing.  You are doomed to frustration, and you will annoy the pig."
Personally, I feel that a new fighter can very profitably spend six months or more training without armor, to learn and hone the basic techniques.  As a case in point, I recently had a student start fighting after training unarmored for about nine months, while he made his armor.  When I watched him fight in this third armored practice, he was already more effective than two of his friends who started fighting in armor after only a short time of unarmored training (they started much later than he did).
I recognize that this is counter to the “get them in armor fast, so they’ll stay interested” viewpoint.  Again, that is a choice – for the trainer, this time.  My bias is that I'm trying to get my students to achieve the optimum, or at least to have the basis for doing so.  I feel that a good foundation of basic techniques is necessary for this.  Many people don't share my goals or point of view, and I do not expend much effort in trying to convince them.
Also, your kingdom may have requirements in place that necessitate authorization in S&S before other weapons can be attempted.  The West doesn't, but you should check with your local marshals. 
As a note on a related topic, if you have a small fighter (especially those who are short), who is also relatively weak, please:

1. Don't load them down with so much armor that they can't move.  While it is very necessary to have them well protected, if they are carrying half or more of their body weight in armor, they are not going to enjoy the experience, or be effective.  Use lighter weight material, where possible. 
2. Don't give them a shield so big that they can't carry it, and can't swing around it.
3. Don't give them a short sword.  The shorter fighters need longer, medium-weight, tip-heavy swords to generate power and get range.  With a short, light sword, they will never be able to hit hard enough.  With a short, heavy sword, they won't be able to swing fast enough to hit anything. 
4. Don't encourage them to "be aggressive, and fight as close as possible".  That makes them vulnerable to the effects of the strength and weight of larger, stronger fighters, as well as making it almost impossible to protect themselves from high wraps.

They should be aggressive in getting to and maintaining a position and distance that allows them the greatest opportunity to use their techniques.  For shorter fighters, this is usually about on the boundary between A and B range (depending on how you define them).  Also, a position on either corner of your opponent is better than being right in the middle.

Questions about Training

To provide some perspective, here are some questions that I recommend trainers answer, before they start teaching.  You should be aware of these questions, so that you will have a framework in which you can more easily ask your own.

1. Do you know why you teach a certain technique?  Is your only reason:
1. "It works for me", or
2. "It's what the fight books say (I think)", or
3. "That's the way I was taught"?
2. What are the advantages and disadvantages of using a certain technique? 
1. What are you giving up to gain the advantages? 
2. Will that technique fit in with the other things I do (or should be doing)?  Is that technique part of a cohesive system? 
3. Will it only work on lesser-skilled opponents?
3. If it works for you, will it work for another fighter who is not as strong, or not as fast, or not as agile, or not as tall, or not as skilled?
4. Is the continued use of the technique going to eventually cause injury to the user because of
1. Repetitive stress,
2. Applying torque to a joint in a bio-mechanically unsound position, or
3. Over-stressing a smaller muscle group when a larger one should be used?
5. Do you know an effective way to teach that technique? 
1. Do you know two or three ways, because not everybody will understand only one way? 
2. Can you teach techniques that you don't use - because that technique may be great for a student with a different skill set?

Transition from Karate

New fighters who have experience in one of the Asian striking arts – Karate, Kung Fu, Taekwando, etc. – often seem to have more trouble adapting to heavy weapons fighting. 
The problem seems to be the timing of the power application for blows.  In the striking arts, the hip usually moves well ahead of the hand, providing a whipping acceleration.  This creates a problem when using the heavy swords, because as you pull one end sideways, the other end tends to flip strongly in the opposite direction.
Many advanced practitioners minimize the timing between hip and hand movement, even though the sequence of body movement is the same.  With single blows from a static position, this can be effective when using a sword. 
However, it is also very important to pull the sword into a swing by pulling towards the hilt end of the sword, so that during the initial part of the swing, the sword moves along its own length.  In many techniques, especially during combinations, the sword should move in a slightly circular path, which is not the case with the blows in many of the striking arts.
Strangely enough, all of these requirements seem to be present in the way beginners in the striking arts perform a step-punch.  The hips move nearly simultaneously with the rest of the body.  The abdomen remains tight from the initiation of the movement to the end.  The hand and sword move in a slightly circular path.
If you’re transitioning from one of the striking arts, and having less success than you expected, consider what I’ve said, and experiment with it.