Without supplemental light it's hard to get fruiting or root vegetables to do much in winter indoors. I'd say skip the carrots and try the tomatos only if you have a grow light. Even the broccoli, that is cold-hardy, isn't likely to get enough energy from the weak winter light to put out much of a head.

Lettuce (broadcast in pots for cut-and-come-again growth) is the only vegetable you mention that may do OK but only if you have good southern exposure in your spare room. I've been able to grow lettuce, arugua, thyme, etc. in pots on a window sill, but the slow growth in the low light conditions in winter makes it pretty unsatisfying.

You're better off growing sprouts, or following the winter harvest techniques described in Eliot Coleman's "Four Season Harvest." The point of his book is that you focus on ways to harvest fresh vegies that you've grown during better growing conditions of the other seasons, rather than trying to grow them in winter.