You know enough to know what you need, which is power and speakers. You already have a mixer, and you are right, you can't just plug speakers into it.
Just a little info. There are a few basic ways to go.
1. Separate components. Speakers, mixer, amp. This offers most flexibility in terms of selection, and allows you to upgrade components one at a time as budget and needs dictate, or rent/borrow to add on for larger shows. Another plus is that there are tons of used speakers and power amps out there, and you can get good stuff used. The drawbacks: this kind of system takes the longest to set up. It is the bulkiest to carry around. You should put your amp and mixer in cases for protection. This costs more money. If your mixer is part of your studio you need to rip it apart for gigs, and set it back up to record, and the same if you want to practice.
2. Powered mixer plus speakers. This is a mixer with a power amp built in. Plug in your speakers and go. They generally are built into pretty rugged boxes so they don't need any case. These have been around for awhile as well, plenty of good used stuff out there. If you buy a bigger system they are great for monitors or practice. Drawbacks: Upgrading the power or the mixer requires you to replace both at once, as they are in the same package.
Older ones don't sound that great.
3. Powered speakers plus mixer. The speakers have the power amp built in. Plug in your mixer, plug in speakers, off you go. These are pretty spendy, and haven't been around very long, so they ain't cheap even used. Very simple and sounds great. You get to use your nice mixer, so it sounds good, but still have to break it out of your studio.
No matter what $400 is probably pushing it, especially to get over drums. Look for some used speakers and a power amp in your area, and make sure you get to hear the stuff first, if you want to go the component route. Another option is Fender Passports. A kind of all in one unit. I've heard and gotten good results with these. Get the 250 if you go this route. They also have decent resale, and like the powered mixer scenario, they make a great practice PA when you upgrade. I'm not a big fan of Carvin PA gear. Musician's Friend has some basic PA packages you could check out, just avoid the Kustom junk.
Thes packages are a good way to start, just look at each and budget for mic or speaker stands.
Have fun!
