Bigped51 said the most important thing although others brought it up as well. Read the first 100 or so pages of a current reloading manual. Read it again or read another one. Pick out the caliber you shoot the most of and find where to source bullets. That is by far the most expensive part, especially for a beginning reloader who really doesn't know what they want. You are not going to be buying huge quantities right off the get-go so there is no real savings by buying bulk to get free shipping. Shipping is expensive. Next up is sourcing gunpowder and primers. If you can't get these locally then they will have to be shipped and hazmat fees really make such items expensive in small quantities. Hopefully you can find bullets, primers and powder locally. Yes, getting all this (and more) is expensive to start up.
With that knowledge go out and buy a press, I would suggest the same as dirtybarry, a Lee Classic Turret Press. Get the kit version, it comes with the Lee manual so buy the Lyman or Sierra or Hornady in the initial learning phase (unless you buy the Turret kit based upon what I say here. While I am not thrilled with the Lee balance, you can replace it with something better down the road. For now it works. I do like the autodrum kit. It works very well considering it is measuring by volume. If it doesn't come with dies, you will need to buy them as well. Remember, start with one caliber, master it, then add others later by purchasing a new turret for about $15 and a new set of dies. The 4 die carbide Lee ultimate dies for straight wall cartridges when starting reloading are worth the few extra dollars. The Lee Turret is a simple press that can easily and very quickly be switched from one caliber to another. While not a progressive press, it is somewhat automated yet still retains the capability of operating as a single stage by removing the drive post in a matter of a few seconds. I too still have mine. I have lost count of the number of rounds of .357M .45ACP, and .44RM it has made. I still use it for all my straight wall cases like .45-70 and I still use it for the 30-30 although I used it for a long time to load a lot of .308, .223 and 300WM as well. There are a lot of presses, but the Lee Classic Turret Press has earned its valued spot in my reloading room many times over.
Other presses have come and gone. If you KNOW for certain that you are going to shoot a lot of handgun, then a progressive press might be useful. I would strongly suggest waiting until you know for sure. Most of them are finicky buggers for changing out calibers, it can take some time to do so and then re-tune the press for that caliber. They can require several expensive parts (so-called 'conversion kits' in Dillon speak) specific for each caliber. I eventually left my Dillon 650 set up for .357 all the time. While I had conversion kits for .44 and .45ACP, I found the process involved was just not worth it. One can get the Lee Turret to crank out around 200 to 250 quality rounds an hour while the Dillon 650 could do double that, but the half hour spent changing it over and then fine tuning it to work smoothly I found to be a pain. If you are making 2000 rounds of one type at a sitting then the Dillon might be the way to go at some point, but when you start out, you won't be.
Once you have the press, read the reloading manual and play with the parts. Take the dies apart and look at them. You will want to clean and oil them before first use anyway so you might as well know how they work. Put it all together, dial it in while operating it 'dry' (no powder, etc) to see how it all operates while reading the manual. Once you feel comfortable, fill it up with the goods and start making ammo.
Anyway, lots of good info in the replies above too. Choose something, but be sure to choose to read the manuals, watch some youtube videos, and come back to ask more specific questions, etc. Lots of good info that isn't covered in the manual and of course there is the personal learning curve with the different presses and accessories as well.