We're looking at the big picture, this is a how to buy an audio system that best suitsyour needs. So while I'm not going to recommend specific products, I'll set you on a course of action.
Step 1: Think.
What room in your home do you want to listen to music or watch movies? True, most folks may have only one or two possibilities, but if you have a lot of options, that's great. Larger rooms tend to sound better than small ones, but try to avoid rooms with wide expanses of bare floor, exposed large windows or mirrors, all of those highly reflective surfaces are bad news for sound.
If possible, don't place speakers directly up against a wall, or in a corner. Again, if you have some flexibility about which wall in a room you can place the main (front left and right) speakers, you'll improve your chances for hearing the speakers at their best. Keep your options open. Thinking about all of this before you buy anything is a crucial first step
step 2: Music only? Or movies? Or both?
If you listen to more music than movies, stick with two speakers, along with a stereo receiver or amplifier, plus a CD or digital music source like your computer or smartphone, and if you're into vinyl, a turntable. Your budget invested in two speakers rather than five or more speakers allows you to buy better quality speakers. I use a stereo home theater at home, and never once missed having surround sound, but I listen to at least 10 times more music than movies.
For home theater, you might want to keep it simple and buy a sound bar, and there are a lot of possibilities, from very moderately priced bars to high-end ones. Still, if you want to hear movies and TV shows at their best, you can't beat a multichannel system with five or more speakers, a subwoofer and a receiver. The sense of immersion a bona-fide multichannel system can provide will be miles aheadof even the very best sound bars.
If you've convinced yourself to go the wireless route, cool -- just understand you're paying more for inferior sound quality relative to normal wired speakers. Oh, and last time I checked, wireless stereo and home theater speakers each have at least one wire, the one you plug into the wall for AC power.
Some folks might even want to invest in a Dolby Atmos or DTS:X home theater that can also produce height effects so the sound can appear to come from above you. These systems typically have seven or more speakers, a subwoofer, plus a Dolby Atmos or DTS:X ready receiver. There's a lot to think about, so it's best to plan ahead to see what works best for you. Of course, the more speakers you add, the more complex and more expensive the system will be.
If all of that sounds like more than you bargained for, again consider a stereo home theater, with justtwo good quality speakers, and possibly a subwoofer. If your budget is tight, a sound bar is probably the most cost-effective approach.