Right OK, I'm no nutritionalist but the info I give is from reliable sources (and I can reference most of them if needed) and I have chrone's disease so I have to be aware of nutrition, so:
If you won't eat veg, you will have to up the fruit - be that juice or actual fruit. If you are worried take a general vit supplement.
Make sure you have breakfast, its always good to get a balance so it might be worth having say - toast and a boiled egg (if you are worried about cholestoral - take a lecithin supplement).
Make sure you don't have too many carbs in your diet, for someone training (it's a little different if you are less active) try a 50% Carbs, 30% protien, 20% fat (I will double check these figures but that sounds right off the top of my head) Remember the fat has got to be good - no hydroginated fats (sometimes called trans fats) and no saturated fat - so try and stick to olive oils etc.
Now, not too many carbs - for two reasons, one, carbs make you fat and two, if you feel sleepy after a meal - it's probably because you have too many carbs in. Also it's better to have carbs after workouts rather than before - as during training fat will be burnt as energy, after the carbs will replenish glycogon stores.
Protein, don't overload on red meat as its hard to digest and will sit in the gut (maybe one portion a week). Chicken is good (not fried) and other meats. Protien are like building blocks, but you still need the cement and water (the carbs and fat) to rebuild.
For fats - try cooking etc. with olive oil - its great. Try and avoid margarines if poss as they contain trans fats.
Dairy - now some say don't have too much dairy which I can go with, but they are an important source of calcium and protien as well as a ruck of other nutrients.
Ok,as for being picky about food you have two options:
1. Not get anywhere with your training and carry on feeling tired and probably end up quiting because you feel so bad.
2. Bite the bullet and get eating - if any one normally says to me 'I don't like fish' I say what fish? They all taste so different, then how many different ways have you tried it - poached tastes different to fried - a lemon sauce is different from parsley and scampi, cod, plaice, tuna all taste very different. (good example I hated spag bol for years, then cooked it myself and realised what a few extra ingredients can do - try different recipies there is a whole world of food out there that you are missing out on!!).
As an alternative you could spend a lot of money on supplements that will provide you will nutrients (that you could get from a normal diet).
If I were you I would invest in a book or go and see a nutritionalist, I would try boods from http://www.stadion.com/
Hope this helps.