A good home theater on a budget is mostly about spending in the right order. Most people put too much into the screen and too little into sound, then wonder why movies still feel flat.
Start with the room, because it costs nothing. Sit at a distance where the screen fills a good share of your view. A common rule of thumb for a 4K set is to sit roughly one to one and a half times the screen's diagonal away. A 65-inch TV seen from ten feet looks smaller than a 55-inch set from six. Measure your seating distance before you shop, and buy the size that fits it.
For the picture, a mid-range 4K TV is the budget choice. It needs no dedicated dark room, works in daylight and has streaming apps built in. Projectors look like a bargain per inch, but a bright enough one for a room with windows costs more than people expect, and you still need a screen or a smooth white wall.
Sound is where the money should go next. TV speakers are the weakest part of almost every set. A soundbar with a separate subwoofer is the simplest real upgrade, and it matters more for dialogue than for explosions. If you can, pick one with a dedicated center channel, because that is what keeps voices clear.
If you want to go further, a used AV receiver and a pair of bookshelf speakers often beat a soundbar at the same price, and you can add a center, surrounds and a subwoofer over time. Surround sound is a place where secondhand gear holds up well, since speakers do not age like electronics.
Do not overspend on cables. Any certified HDMI cable carries the signal, and an expensive one will not improve the picture. Spend the difference on a few acoustic panels or a thick rug instead. Soft surfaces reduce echo and help cheap speakers sound better.
Lighting is the last cheap upgrade. A dim lamp or a bias light behind the TV makes contrast look better and eases eye strain.
The short version: measure your distance, buy a reasonable 4K TV sized for it, and put the rest of your budget into sound. A soundbar with a sub is the fastest win. A used receiver with bookshelf speakers is the better long-term path.