I'll support the remarks about taking courses, climbing with experienced people, and taking the time to learn things well before you get very serious about winter mountaineering.
In the right conditions you can sometimes travel steep terrain in light shoes and crampons, sometimes it's faster and easier than boots and sometimes it's slower and more dangerous. You probably shouldn't try until you've climbed enough to be able to figure out when it would work and when it wouldn't, and you won't get that experience without owning at least one pair of boots.
When cramponing in certain conditions you want a lot of support. Standing in two-inch deep steps kicked into a 50-degree slope takes noticeably less energy, concentration, and calf strength in stiffer footwear. If you have a lot of it to do you will wish for something rigid.
Crampons come in a lot of variety these days. Avoid the ends of the spectrum, the super-fancy steep ice and mixed crampons and the super light and flexible crampons, until experience leads you to want specifically that. The steel 12-point crampons discussed, along with the beefier 10-point models (Petzle Irvis, BD Contact, Grivel G-10), will serve all of the needs of 90% of mountaineers.
By the time you have enough experience to use the broad variety of equipment and techniques that are available with safety you will probably own a truck-load of gear anyway, so don't sweat to much about getting it right the first time. Actually, I'd say whatever pair of steel crampons you can find used for around $50 will probably do just fine for your first pair, as long as they will fit on whatever boots you get.

