Screws are not a good way to achieve alignment. You can’t locate the holes that accurately, particularly by hand. Even with a drill press it would be difficult.
Biscuits aren’t that good either and you would need a $200 biscuit cutter, which in my opinion is not a very good investment.
One of the best ways involves complex cuts with a corner lock miter bit, but that requires a router table.
So what’s left, and it’s actually very good, is using dowels. But you need a quality doweling jig and there are only two that you should consider.
The Dowelmax Jr jig for $109 or the Jessem jig for $130. I use the Jessem, but the Dowelmax is fine as well.https://jessem.com/collections/joinery-systemshttps://www.dowelmax.com/product/junior-dowel-jig-2020/
Don’t even consider any doweling jigs under $100. Particularly the Milescraft products. They are all junk and won’t do the job of getting good edge alignment.
Dowels will also add strength to the joint that you won’t get with simple butt joints.
The Track Saw that jcsperson recommends for cutting down the sheet goods is rather expensive. About $430. There is a cheaper one that recently came on the market from MCLS for $160. I have no idea if it is any good or not, so I’m not necessarily recommending it. Just letting you know about it. Grizzly also sells one that is priced in between these two. I use a Festool system, but that cost is probably not going to make much sense for you unless you plan on doing a lot of woodworking.
Since you have a DeWalt sliding miter saw that might take care of all the crosscuts you’ll need unless the cabinet is very wide or deep. So you might be able to get your local lumber yard to rip down the sheet goods to the needed width dimensions and not have to invest in any new saw at all.
Finally, I’m a big fan of Baltic Birch plywood over MDF. In fact, I won’t let MDF into my shop for any purposes. And there are others who agree with me that BB is much preferred for speaker cabinets.