Here's a checklist of the things you'll need and/or want to get your first Raspberry Pi up and running:
The Pi itself. The Raspberry Pi 3 has built in bluetooth and wi-fi, which is super nice, and a noticeably more powerful CPU, which is also super nice. There are a bunch of other versions of Pi that may suit niche uses better, but in general the Pi 3 is the one you want.
A HDMI monitor. Doesn't need to be anything fancy.
A keyboard and mouse. You might want to use bluetooth to keep your USB jacks open for game controllers. Or you might want to use a wireless keyboard/mouse combo that shares a single USB dongle. The ones that come with their own dongle are less likely to run into compatibility/driver issues, and sticking with well known name brands like Logitech is a safe bet too.
A micro sd card. This is the main drive on Raspberry Pis, and where you'll install your OS. I like to use 32 G cards because it gives a reasonable amount of room for downloading movies and what have you.
An OS. I highly recommend sticking with
Raspbian as a general purpose OS, and NOOBS if you're interested in testing out the more niche OSes.
A USB power supply. Any generic micro USB phone charger will probably work, but if you want something that's not a cheap piece of junk look for
one that can supply 2A or more. It's not super critical to have a beefy power supply, but if you're going to use all 4 USB jacks then you'll definitely want to avoid the bottom of the barrel chargers here.
A case. I have
this one. It's $8 with a lid. You can spend a lot more on a case if you want something made out of aluminum or whatever, but this one is not the shittiest case around, and the price is right.