VirginiaTim,
Depending on how much you want to grow, you may consider shelving. That way you can have a central location and set up grow lights (quite inexpensive). Hydroponics is certainly an option as well.
Technically, you can grow anything in a container. Since you are looking for smaller root systems for space efficiency, here is a list of vegetables for container gardening:
You can grow many cultivars of vegetables in containers and they don't have to be miniature because they have shallow root systems...
Vegetables for Container Gardening
Beans: Bush Romano, Bush Blue Lake, Tender Crop, Royal Burgundy, Henderson Bush, Jackson, Wonder Bush, Topcrop, Greencrop, Contender, (Pole) Blue Lake, Kentucky Wonder, Bush Romano, Bush Blue Lake, Tender Crop, Lima: Henderson Bush, Jackson, Wonder Bush
Beets: Little Egypt, Early Red Ball, Asgrow Wonder,’ ‘Detroit Dark Red,’ ‘Greentop Bunching,’ ‘Monoking Burgundy, Red Ace, Little Egypt, Early Red Ball, Early Wonder, Detroit Dark Red, Boltardy, Burpee Golden
Broccoli: Green Comet, DeCicco, Green Comet, DeCicco, Spartan, Italian Green Sprouting
Brussels Sprouts: Jade Cross, Long Island Improved
Cabbage: Dwarf Morden, Red Ace, Early Jersey Wakefield, Dwarf Modern, Red Ace, Early Jersey Wakefield, Little Leaguer, Earliana, Copenhagen Market, Ruby Ball Hybrid, Red Head Hybrid
Carrot: Short & Sweet, Danvers Half Long, Tiny Sweet, Royal Chantenay,’ ‘Red Cored Chantenay,’ ‘Long Type Chantenay,’ ‘Danvers 126’ and ‘Orlando Gold, Baby Finger Nantes, Goldenhart, Little Finger, Royal or Red Cored Chantenay, Ox Hart, Baby Finger
Chinese Cabbage: Michihili, Burpee Hybrid, Michihili, Burpee Hybrid
Cucumbers:Burpless, Liberty, Early Pik, Crispy, Salty, Patio Pik, Spacemaster, Pot Luck, Bush Whopper, Bush Champion, Burpee Hybrid, Salad Bush, Parks Burpless Bush, Burpless Early Pik, Patio Pik, Spacemaster, Pot Luck
Edible Flowers
Garlic Most Varieties
Green Onions:Beltsville Bunching, Crysal Wax, Evergreen Bunching
Herbs
Lettuce:Buttercrunch, Salad Bowl, Romaine, Dark Green Boston, Ruby, Bibb, Green Ice, Red Sails, Lolla Rosa, Buttercrunch, Nevada, Bibb, Parris Island Cos, Salad Bowl, Slobolt, Tendercrisp, Black-Seeded Simpson and Oakleaf, mustard cress, Salad Bowl, Ruby, Grand Rapids, Oak Leaf, Buttercrunch, Dark Green Boston, Little Gem, Bibb
Onions: White Sweet Spanish, Yellow Sweet Spanish
Parsley:Evergreen, Moss Curled
Radishes: Champion,’ ‘Red Prince,’ ‘Scarlet Globe, Cherriette, White Icicle,’ ‘Chinese Winter, April Cross, ‘Easter Egg, Red Flame, Cherry Belle, Icicle, Cherry Belle, Icicle, Champion, Scarlet Globe, Cherry Belle, Scarlet Globe, (White) Icicle
Spinach: Dark Green Bloomsdale
Peppers:Yolo Wonder, Keystone Resistant Giant, Canape, (Hot) Red Cherry, Jalapeno
Eggplant:Florida Market, Black Beauty, Long Tom, Slim Jim, Ichiban, Slim Jim, Ichiban, Black Beauty, Modern Midget, Mission Bell, Small Ruffled Red, Thai Green, Bambino, Sweet Banana, Yolo Wonder, Long Red Cayenne, Sweet Banana, Valencia (Hybrid), Jackpot (Hybrid), Camelot, Jalapeno, Red Chili, Giant Thai, Super Cayenne II, Sweet Banana, Yolo Wonder, Long Red Cayenne, Bell Boy, Keystone Resistant, California Wonder, New Ace, Red Cherry, Long Red Cayenne, Jalapeno, Thai Hot
Squash

ixie, Gold Neck, Early Prolific Straightneck, (Green) Zucco, Diplomat, Senator, Scallopini, Baby Crookneck, Creamy, Golden Nugget, Gold Rush, Zucchini (most varieties)
Tomatoes: Tiny Tim, Small Fry, Sweet 100 Patio, Burpee's Pixie, Toy Boy, Early Girl, Better Boy VFN, Agriset 761, Better Boy, Celebrity, Colonia, Mountain Fresh, Mountain Gold, Mountain Spring, Park’s Improved Whopper, Sunbeam, Solar Set, Sanibel, Captiva, Sunleaper, Suncrest, Sunrise, Sunpride, Terrific, Cherry Grande, Mountain Belle, Small Fry, Sweet 100, Peto Hybrid 882, Plum Dandy, Tropic, Caruso, Laura, Jumbo, Tropic, Vendor, Tiny Tim, Small Fry, Sweet 100, Patio, Burpee's Pixie, Toy Boy, Early Girl, Better Boy VFN, Pixie, Red Robin, Sugar Lump, Tumblin' Tom (hanging baskets), Patio, Pixie, Tiny Tim, Saladette, Toy Boy, Spring Giant, Tumbling Tom, Small Fry