I started out with the Lee Challenger Anniversay Kit and I see that they have improved it with their breechlock system. Many, many reloaders have started out with the kit and still use it years later. I still use most of the tools that came with the original kit: It was one of the the best investments I have ever made, years of fun.
If you don't have a place to mount it on a bench, I have found that the utility room is a good spot.
If you don't want to go to the trouble of mounting a press:
Lee Breech Lock Hand Press. This is a hand press that you use without mounting. My second press, this is the equipment that really taught me how to reload better than most reloaders. You can feel everything that is happening in the cartidge and it is easy to use. It will fit in a field bag with dies too, so you don't have to quit when you run out of ammo (always happens to me), just keep reloading.
Lee Classic Loader: My favorite equipment and the one that I use the most. It fits in your back pocket or field bag with the addition of a hammer (12 oz at home, RCBS 4 oz in the field). Or you can use a branch, a stone, the jack from your car or truck, tire iron, anything that is heavy. It consistently produces ammo that is competition quality. There are a lot of good shooters who use this equipment as their main reloading machinery. I can currently produce a round in about 25 seconds so it is not slow as some claim. The rounds produced will work well in a single shot rifle, but because they are neck sized only, don't work as well in a sem-auto as the cartridge needs to be resized to standard specs. Currently selling for about 24.99, btw.
I found, when I started out reloading, that it is far easier than I expected. Dirt simple. A lot of research on the internet can make it sound much more complicated that it really is. Just read the instructions and follow them to the letter and you will have better ammo than you can buy. Using the Lee Classic Loader, I have put ten rounds of 45-70 through a single hole at 100 yards, which simply won't happen with factory loads.
I paid back my intial equipment cost on the 111th round, day one. At current ammo prices, the payback would be 80 rounds or so. My cost for a reloaded 45-70 round is about 14 cents per round rather than 2.00 per round factory loads.
I would start out with the Lee Challenger anniverdary set as that will teach you the craft and then go to a bigger press or do as I have done, go to a smaller outfit.