A lot of the posts here have been really gear focused. I'll answer your question first, but I think the bigger question is how to get yourself into the habit of cycling regularly. I ran in high school and xc in college. I still run recreationally but started bike commuting and got into going on long rides with some more competitive guys.
As far as fit goes, don't feel the need to decide now. If you buy at a shop they'll let you take models out for a test ride. Generally speaking endurance bikes will have a more upright position, while performance bikes will have a more aggressive position. Think of it like wearing a really padded trainer vs. a racing flat only to a much greater effect. A more aggressive position pushes you forward on the pedals and makes you go much faster.
The biggest thing in buying a bike is to get help from somebody who knows what they are doing. Ideally, if you have the money, do that by buying from a local bike shop and getting a professional fitting. There are so many variables beyond just size (stem length, saddle position, bar width, q-factor, etc.) that it's important to get right if you're serious about riding a lot of hours.
The biggest challenging in transitioning to cycling is the number of hours involved. To get in a decent long ride on the weekend you really need to spend a lot of hours on a bike. Let's say you're in decent shape and want a medium distance work out. That might mean 3 hours for a sixty mile ride, plus a little for any stops. That's almost half a day on your bike.
So as others have said find a local bike club. A lot of clubs and shops have different rides at different speeds. The advantage compared to running is it's a lot more social. If you want to ride enough to stay in good shape shoot for around 150-200 miles a week. When I'm just cycling and not doing much running I might ride 5 days a week, with the following types of rides: 1 weekday after work group ride (either hills or sprints around a local loop) maybe 20-25 miles, 1 morning or afternoon solo ride - 25-30 miles, 1 trainer ride - 20-25 miles, Saturday solo ride - 30-40 miles, Sunday group ride - 40-80 miles. I'll mix intervals or climbing into the weekday rides, and occasionally I'll drive somewhere to get some serious elevation for one or both of the weekend rides.