Wow, that is a lot of pages! I was interested to see what the initial feedback was from the Op's question, but i get the feeling that not everyone agrees. ;-)
Bike weight makes a difference to performance (try racing on your 11kg winter bike!). So one can assume wheel weight makes a difference as part of the bikes overall
weight.
The faster a rider travels the more air resistance he or she is going to encounter. Most races are on the faster end of the general cycling scale. Aero trumps weight in most cases.
There are many factors to consider in picking your wheel but in general one might concern themselves with material, width, depth, spoke count, warranty and build process - ie hand built or factory. All of these make a difference in terms of performance and feel. All of this is quantifiable. Obviously imo.
"Get a coach" is good advice if you are in a position to do so. Do as you are told and follow a pretty strict program. If you are just fancying giving racing a go and also fancy the idea of some new wheels then perhaps "getting a coach" isn't the best advice available.
Finally i would add that if anyone is suggesting that a £100 pair of 15mm deep 2 kilogram wheels with gatorskins offer the OP the same performance as a pair of wheelsmith tubs (38mm - 1200 grams) or (38mm clinchers - 1400 grams) with quality tyres, then i'd suggest trying the two wheel sets out over a set distance and seeing the difference. Same goes for 50mm versions. I have a power meter and good wheels and shitty wheels, shitty tyres too, and i can freely tell you that a significant gain or loss can be had by choosing certain tyre and wheel combinations. Position on bike makes a huge difference too.
Perhaps get new wheels and a coach. ;-)