Hornychief - Three general types of reloading kit. No, make that four.
The Lee Loader is the simplest and fits in a small box. It turns out good ammo, but involves a lot of manual effort (including hammers) and is slow. On the other hand, it can get you into the game for maybe $30-40 plus the cost of components. It's made in many different calibres, but each one is specific. Nothing wrong with the ammo it produces.
The other three use interchangeable dies. Buy a new set of dies and you can start making different calibres.
The single stage press is the most common and commonly uses three-die sets. You run a bunch of brass through one die, swap dies, run them through the second die, swap dies, run them through the third, etc. It's faster than a Lee Loader and allows greater versatility. You also don't need to use a hammer... Most people start there and don't ever get anything more complex. They (and the others) have the advantage, once you get the press, that you can buy a new set of dies and start reloading another calibre.
The top-end type is the progressive, in effect a miniature ammo factory. So long as the bins with primers, powder, brass and bullets are kept full, every time you pull the lever, you get a complete round of reloaded ammo. If you are shooting a lot, it's a real time-saver. On the down-side, they're more complex and considerably more expensive. Most people don't ever get that complicated.
In between is the turret press. It is in effect a single stage press but with a set of dies mounted in a quick-change plate, allowing rather more speed and ease of changing dies.
If you haven't already done so, I would strongly recommend a large paperback called The ABCs of Reloading. It's arguably the best introduction to reloading on the market. You would be well-served by buying one (many editions, all good) or signing one out from a library. Many questions are answered.
I put together an Excel costing spreadsheet for ammo reloading, showing things like cost per round, payoff time, etc. If you are interested, PM me with your email address.