Depends whether you want and Dolby or DTS decoding for surround effects. If you do then you’ll need a new amp (an AV amp) and at least a good centre speaker and 2 OK rear speakers in addition to the 2 stereo speakers I’ve guessed you already have.
If not, then you can just plug your new TV’s stereo out into a spare input on your current amp and enjoy it in better stereo than the TV will manage on its own.
You don’t say what sources you have like DVD, BluRay, Sky or cable, free view box. This might help. If all you’re after is better sound than your TV’s speakers then, yes, a soundbar will be a bit better.
If you’re considering starting over and TV is what you’re after, rather than ‘Hi-Fi’ then your choices are wide and simple: get a big LCD TV with LED backlighting; get an AV amp or AV receiver; get a 5.1 set of speakers. You could go for 7.1 or 7.2 but it means more speakers, more clutter and there are few 7.1 BluRay releases. Don’t get carried away with lots of nonsense about cables. Just get fat cable for the front & centre speakers, OK cable for the rears and a regular HDMI cable for each of your sources from eBay or amazon.
you could spend anything from about £1000 & up. Sure you wouldn’t prefer a new bike?