First off, I would PLAN which calibers you load, but start with a SINGLE caliber.
I would start with 9mm for several reasons:
1. Expense. Plated (or Lead) bullets are cheaper, powder is cheaper since you use 1/5th as much. You can load 9mm for half the cost of cheap russian stuff without trying. With .223, you almost break even. Unless you have the skill and equipment to take advantage of accuracy gains in .223, I would hold off for now.
2. Complication. Loading rifle correctly is much more complicated. For most .223/5.56 ammo, you will need to:
clean, lube, size, clean, trim, chamfer, deburr, remove primer pockets, prime, and load.
For 9mm you need to:
clean, prime, load.
3. Tools required. Rifle requires many tools you simply do not need for Pistol.
When you start loading, choose your press carefully. You will need to choose between Single-stage, Turret, or Progressive. Most folks end up loading Pistol on a progressive, rifle on a turret or single stage. I started by loading pistol on a progressive. I do not regret this, and I did not have problems. I still load pistol on the same type of press. If you are careful and meticulous, any type of press will be just as safe. I have made less loading mistakes on a progressive...it is pretty much impossible to accidentally skip steps. If you start with a progressive, they can work almost identically to a turret. Just load 1 casing at a time onto the shellplate and you are only doing a single task at a time.
Brand of equipment. This causes the most conflict of any topic in reloading. Like everyone, I have my preference, but I won't fixate on it. I'll just give you guidance. The two ends of the spectrum are Lee and Dillon. Lee is cheaper, but can be more temperamental. Dillon has a reputation for reliability, but you pay for it. Both make the same quality ammo. If you take pleasure in working on your own car, figuring out mechanical problems and tinkering in general, get the Lee. If you would rather buy something expecting it to work perfectly out of the box, and sent it out for repair when it doesn't, get the Dillon. RCBS and Hornady have a fine reputation, and fit somewhere between these two. I don't know as much about these, mostly because they don't have RCBS vs Dillon arguments every week on forums. Dillon has a lifetime warranty. Lee doesn't...but Lee parts are very inexpensive to replace.
RMR Reloading is a good place to start for projectiles. I buy both Rifle and Pistol from them these days - they beat just about anyone else's prices for the stuff I buy. And they support THR. And they give THR members a discount.