You can go either way, take a class or get somebody who knows what they're doing to teach you the basics.
I started on a progressive press without a class. But, my son and his buddy reload, so they came by and helped me set it up and showed me how the press worked. Once you understand the mechanics of assembling a round, it's pretty straight-forward.
It's VERY important to look up the specs on the round you want to load, (and I'd use at least two sources in case of a typo/misprint). Do some reading so that you understand what COL is, what starting charge means and what max charge means.
Put together a list of what you need. Obviously a press, and people can argue all day about whether you should start with a single stage or a progressive. So, pick a press, get the die set. Then you'll need at a bare minimum a decent scale and a micrometer. You'll also need brass, powder, primers and bullets. Depending upon where you are, you may have issues getting some of those. Primers are in short supply everywhere right now, and some companies don't ship to Massachusetts.
You've said that you're interested in loading 7.62 and 5.56 plus some pistol rounds. I'd probably start with a pistol round, a straight walled one such as 9mm, .38spcl or .45ACP. Bottleneck cases are a little trickier to crimp, so I'd get the basics down on an easier round first.
Set up the press, adjust the dies according to the mfg or to videos on youtube. Work with some empty brass, (no primers, no powder). Get the flare set and get the crimp and seating set, verify the OAL. Seat a primer in a case and setup your powder drop. Cycle the same case through at least half a dozen times, make sure the powder drop is consistent.
Assemble a dozen rounds or so, checking the powder drop and the OAL on each as you work them through the stations.
Take them to the range and chrono them. Pick up your brass and look at the primers, (google primer flow).
Patience, repeatability and OCD mentality are your friends. If you undercharge a round, you risk a squib. If you double-charge it, you risk catastrophic failure. Take it slow, pay attention. Do NOT force your press at any time. If it's not moving, stop, examine it. If you force it, you're probably going to break something.
Also, there's a reloading forum here in NES, as opposed to the General forum.
Everything related to reloading
www.northeastshooters.com
EDIT: I just noticed that
@mac1911 already posted this link.