There are so many grow lights on the market that it's horribly overwhelming. Though I have heard of people using regular florescent bulbs, healthy plants really require both blue and red light spectrum, just as they would get from the sun. You can find some good prices on line for grow bulbs which can be shipped to your home. If you really just want to get started, aquarium bulbs have both blue and red spectrum to support aquarium plants and are available at Walmart. They carry them in both spot light and florescent lights. The florescent light bulbs are generally 40 watt T12. Both Lowe's and Fleet Farm carry reasonably priced fixtures for both varieties.
Finding a space in your home to start your indoor winter garden can be as easy as designating a specific corner of your living room and a small card table. I have heard of people cleaning out closets to use as well. An unfinished basement works great and usually will give you plenty of room to expand if you choose, not to mention having your own private space away from kids or plants that may knock over your garden. Make sure you have a way to hang the lights at an appropriate level so your plants don't have to stretch themselves towards the bulbs. Jack chain and S hooks from the ceiling give you an easy and adjustable option.
When choosing plants for your indoor garden I recommend plants that are normally kept as house plants that you may take out to the patio or deck in the summer. You can also bring in your summer annuals in the fall and let them to continue to grow so that you can propagate them throughout the winter either by splitting or cuttings. Be cautious of when you start which seeds. Most perennials hardy to Northern Zones have a specific schedule to follow. Most seed catalogs and packets will give you the average time to germination and the average time to bloom for both annuals and perennials. Many perennials, however do not bloom until their second year.
It is worthy to note that growing under grow lights does not equate growing in a greenhouse. Do your research and harden plants off slowly in the spring. Move them to a greenhouse first if possible.