I've been cutting my own hair for years, after a kindly barber suggested I buy an Oster 76 and Andis Master instead of paying her every 2 weeks.
Seriously - if you can get either of these for a decent price, BUY THEM. They are both "pro" barber clippers and better than most Wahls or other brands you can buy (with one or two exceptions).
You'll also need a set of guards - each "number" is 1/8 of an inch. So, a #1 is 1/8..#2 1/4 (2 * 1/8)..#3 (3 * 1/8) or 3/8s, etc. They make guards ranging from a 0 to an 8 (1 inch). And if you want to get really crazy, the Oster 76 takes detachable metal blades (vs guards) and those go all the way down to 00000 (1/100th of an inch) to a "3 3/4" which is really more like a 3 1/2.
DW has worn a pixie for years and fortunately, I learned to also cut her hair years back after she wasn't able to find anyone decent with women's short hair. Just cut hers for her the other day and it's better than 90-95% of the "pro" haircuts she's ever gotten..that said, it also took me several years and dozens of "bad" haircuts on her to get to that point, so don't expect perfection until you've studied a ton of YouTube videos and have tried it numerous times..
ETA - a very good pair of shears is also helpful..I have the Kamisori Black Diamond but they are not cheap..$400+ for the pair (5' shears and 5' thinners) but worth every penny. Virtually all cuts aside from crew cuts require shears..don't skimp on these..spending the $$ makes all the difference..