We're looking at the big picture, this is a how to buy an audio system that best suits your 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, 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 ahead of 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 just two good quality speakers, and possibly a subwoofer. If your budget is tight, a sound bar is probably the most cost-effective approach.
Step 3: How loud do you listen?
For stereo or home theater buyers this can be a tricky one to determine, because even if you only rarely throw parties or watch movies with lots of special effects that are best enjoyed at shake-the-walls volume, you'll need a more powerful (and probably much larger and more expensive) system than one that will only be played at a more moderate volume. Room size is also a major factor, it's a lot easier to achieve high volume in a small room than a really large one.
If you like to play loud, rule out sound bars, I've never heard one at any price that sounded good played loud. Then again, if you're fairly certain you never need to blast music or movies, small speakers or a sound bar will be all you need.
Bass quantity and quality may also need to be factored in. For music-only systems, I recommend large bookshelf or tower speakers that will generate satisfying bass on their own, or if you crave maximum visceral kicks for music, consider adding a mid- to large-size subwoofer. As for home theater systems, subs are de rigueur.
Or go with the no-speaker audio system.
Speakers take up space, and good receivers or amplifiers can be pricey, so you might want to consider going speaker-less and pick up a nice pair of mid-price headphones and a decent headphone amp. Dollar for dollar, headphones provide better sound quality than speakers.
Step 4: How much would you like to spend?
Before you answer "as little as possible," look back on how you answered the previous questions. If you have a small listening room, never listen crazy loud, and would be perfectly happy with a sound bar or stereo speakers and a small receiver, you should have no trouble finding bliss for under $500, £380, AU$665. On the other hand, a well-appointed stereo music or home theater system could start at four times that amount. If you're looking for maximum fun, the sky's the limit.