For a typical stereo master, you'd want a 1/4" half-track tape at a speed of 15ips speed on 10.5" reels. That will give you about 30-32 minutes per reel - traditionally a vinyl album was made up from two tapes, one for each side of the record.
A lot of people here recommend the TASCAM 22-2 as a starter machine, and assuming it's in decent condition, it will work well for this purpose. However it does only take 7" reels (15 minutes each, or 23 for thinner, long-playing tape) and that may not sit well with the mastering house or wherever you're hoping to sending the tapes. (Of course, if you're not sending the tapes anywhere, that doesn't matter)
The TASCAM 32 is the 10.5" version, but I'd be tempted to suggest the BR-20 which is the more modern, last-generation deck. The Otari 5050MX is another contender, as is the high-speed version of the Revox B77 (or PR99). These are all small desktop machines that don't take up much space.
Professional facilities would usually have a larger machine, such as the Ampex ATR-102, Studer B67, Studer A80, A807 etc. But these are not exactly starter machines.
In my home studio I've used a rather beaten-up TASCAM 32, a Revox B77 that needs fixing, before finally getting an A807. They all have their pro's and cons. I still regret not getting a BR-20 while they were still available brand new, though.
For comparison:
http://dougtheeagle.com/lab/lab2005s.jpg - 32 (right hand side, on its back)
http://dougtheeagle.com/lab/2007.jpg - Revox B77 (right - the '32 is next to it, stood on one of the other decks)
http://dougtheeagle.com/lab/2009a.jpg - Studer A807 (again, on the right)