Try handgun reloading first
Ditto on all of the above advice. I suggest starting with a handgun cartridge at first if you have the choice. It will be a bit simpler.
My recommendation for starting out (I think any brand will work, may want to see what is locally most available. I have used Lee, RCBS and Hornady).
* Reloading manuals, at least two. The best ones for reloading instruction I have seen of the recent crop are Lyman, Speer, and Lee (the Hornady manual is likely very good too). Get the one from the press and die manufacturer you have chosen. Also, download or buy the manual from the manufacturer of the powder you choose. If you can a third manul then try to get the one from the maker of your chosen bullets. If you buy RCBS equipment and load Speer bullets with unique powder, the you just need the Speer maula (RCBS and SPeer are same company) and the online data from Alliant Powder.
* Single stage press unless you are planning to load more than a few hundred rounds per week. A turret press would be good as it is operated as a single stage but has the convenience of holding all the dies in one plate for easy change out for other calibers. Or, if space or budget is limited then get the Lee Hand Press. I started with the Lee Challenger and it has done all my handgun and rifle loading. I am thinking of adding a turret press so I don't have to readjust my dies all the time. But the little Challenger has loaded thousands of rounds for me.
* Dies for the caliber you choose. Get carbide for straight wall handgun cartridgfes such as 9mm, .357, .44, .45. I would get four dies, including the normal three plus a separate crimp die.
* Powder. Get a general purpose powder such as Unique, Universal Clays, Accurate #5, etc. you can load decent loads in almost any caliber. You just won't get the most high powered ones.
* A good scale. get the best you can afford. the electronic ones are very fast to operate, but I get buy with the RCBS 1010. This is about the most crucial piece of equipment.
* A quality dial caliper such as from RCBS, Dillon, Lyman, etc. Absolutely must be able to measure cartridge length to the nearest 0.001"
* 2-4 loading trays to hold the cases during the various steps.
* Some form of primer system. I have used an RCBS hand primer for years but am going to try the RCBS plastic strip APS system with a press mounted priming tool. Or you can get a priming die from any of the die makers.
* Primers and bullets. Keep it simple. Buy at least 200 new cases and several hundred primers of the same brand. get a pack of 500 cast lead bullets in the most common weight (115 or 147 gr for 9mm, 180 gr for .40, 230 gr for .45, and 158 gr for .38 or .357.)Once you get a decent load worked up with one powder and the same case and primer combo, then you can start to vary cases, primers, bullets, and other powders. but start with one set of components and learn on that.
* Two shell holders for your chosen cartridge from the same maker as your dies. Use one in the priming tool and one in the loading dies.
* Powder measure. I use the RCBS with the additional micrometer meter. Like a good quality scale, a good quality measure will save you a lot of frustration and make your sessions go smooth and quick. I use the top of line measure from RCBS, but hear that the Hornady and Redding measures are good too. Lee and Lyman also make them.
LATER ON AFTER YOU START RELOADING THE SAME CASES
At first with new cases you don't need all of the possible tools out there. Later, as you re-use the same cases over and over you want to add some more items.
* Case tumbler and polishing media such as crushed walnuts.
* Primer pocket brush
* Case neck brush (nylon or bronze)
* case gauges to quickly check length and diameter of loaded rounds
If you reload for rifle then you need case lube and a lube pad or lube spray; a case trimmer with whatever accessories needed for your cartridge, and a case neck deburring tool.