At a minimum for loading pistol rounds you'll need
1. A press, start with either a single stage or a turret so only one thing is happening
2. A scale
3. Powder trickler/drop or some other method to quickly and accurately measure charges
4. Calipers for measuring various lengths
5. Die for the caliber you want to load
6. Multiple reference manuals for load data
7. Priming tool, although these are usually built into the press these days
For rifle you should add
8. Case trimmer
9. Chamfer/Deburring tool
10. Case lube and some method for applying (where you can usually find something around the house to use for application.)
There's then the debate on if you need to clean the brass and primer pockets before reloading. I know of people who pretty much do nothing other than decap for pistol loads, but in general I think everyone does some washing for rifle since you lube the things for resizing. This can be as simple as a large ziploc bag with dish soap and water, to getting a tumbler of some kind or ultrasonic cleaner.
A bullet puller is something you should probably get for the inevitable mistakes that will happen while learning. A simple kinetic hammer one works fine, although a press mounted one is better but will tie up a press and you'll be starting with just one.
I would also suggest getting cartridge gauges to check what you have loaded, although pulling the barrel out of whatever you will be shooting and using it to test is probably better (have a new M&P 45 that is having some issues with what my Hornady gauge says is fine.)
Once you get all the tools assembled you can start learning the process. It's really not that hard, but the devil is in the details, where there is often more than one correct answer/solution that will work.
