I live in a loft and I have a common area that has a huge skylight. I want to ask my next door neighbor if he'd consider growing a garden with me since we share the top floor. Do you think we'd have luck? When it is sunny, we get tons of light. What veggies grow best indoors?

You could do it! Lots of people do. Here are some ideas.
Tomatoes, bell peppers, hot peppers, herbs, berries, egg plants etc.
Here is a kit to start.
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http://www.neiu.edu/~ncaftori/benin/nati/silo-on-roof-w-vegetables.jpg
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http://www.gardeners.com/Tomato+Success+Kits/VegetableGardening_TerrificTomatoes,35-776RS,default,cp.html
http://www.gardeners.com/on/demandware.store/Sites-Gardeners-Site/default/Link-Product?sku=37-000
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http://www.gardeninggiftguide.com/indoor%20herbs.jpg
http://www.gardeners.com/on/demandware.static/Sites-Gardeners-Site/Sites-GSC_Products/-/Products/32-707.jpg

I'm not sure which ones grow best indoors, but I just stumbled across this website: http://aerogrow.com It seems kind of cool and is very space saving. I can not personally attest to how good this product is, but the reviews on amazon and a few other places are mostly very good.

Good luck with your garden whichever way you choose!!!

Planter Gardening Tips
http://www.simplyplanters.com/planters/plantergardeningtipsarticle.cfm
You can plant it all..Suppressed only by your imagination.
The easiest would be tomatoes, lettuce, cucumbers on a trellis, carrots and potatoes in large size pots, egg plant ,***** strawberries****
Dwarf patio fruit trees can be pruned to maintain small in size for pots.
Tangerine Citrus 4" Pot - Catalog # 9044
http://www.starkbros.com/access?action=product&productID=9044&collection=0
Meyeri Lemon Plant 4" Pot - Catalog # 3610
http://www.starkbros.com/access?action=product&productID=3610&collection=0
Key Lime Plant 4" Pot - Catalog # 3613
http://www.starkbros.com/access?action=product&productID=3613&collection=0
Bonfire Ornamental Peach 4x10 Pot - Catalog # 8883
http://www.starkbros.com/access?action=product&productID=8883&collection=0
************************
Miniature size fruit trees....
Stark® HoneyGlo™ Miniature Nectarine 4x10 Pot - Catalog # 4498
http://www.starkbros.com/access?action=product&productID=4498&collection=0

Stark® Sensation™ Miniature Peach 4x10 Pot - Catalog # 4499
http://www.starkbros.com/access?action=product&productID=4499&collection=0
OR
Miniature Fruit Tree Assortment - Catalog # 100339
http://www.starkbros.com/access?action=product&productID=100339&collection= 1