Great question, and one that comes up often.
While Veneers are a wonderful option for creating beautiful smiles any dentist with extensive veneer experience will tell you that working on a single tooth is a huge challenge. Using 2-3 Veneers may be equally challenging for a few reasons.
If you are trying to alter the shape on one tooth the dentist will have only the space between the two opposing teeth to create the veneer. This may not allow for the Veneer to be a size or shape that compliments your other teeth and may not look natural.
If your only working on one tooth you are also constrained by the colour of your existing teeth. matching one veneer, or even three , to your natural tooth colour can be challenging and its important to remember that, while your teeth may yellow over time (with diet, habits etc) the Veneers won't. so you may have colour discrepancies with only a few veneers.
Another thing to think about is we (society) generally sees beauty in bi-lateral symmetry. Looking the same on both sides , eye position. ears, nose, etc. all comes into play in what we see as beauty in our society. That being said it would never be advisable to do an odd number of Veneers. If you do decide on only doing a few teeth then stick to pairs to ensure the best aesthetic result.
Now, Orthodontics - before any Veneers should be taken into account I think at least looking at your orthodontic options would be important. There are options in orthodontics and you may not have to have full braces. there are options like active retainers, ClearLine or Invisalign appliances. Some more or less expensive than others.
Find a dentist who is familiar with Smile design. While you may not want a full smile design there may be more options available to you than you think.
I hope this helps.