Any soundbar that supports ARC should get you what you want. If you just leave everything as it is and plug in an ARC enabled soundbar then it should stay working the same way except with the audio then comes out of the soundbar. Now as a matter of my own opinion since you said budget I would suggest to NOT buy one with a subwoofer as your money would be better focused on one that has better dialog and a full midrange than one that shifted some of cost to a speaker that has zero chance of reproducing anything close to a powerful impact that a sub is suppose to bring you. Subs that are worth listening to/feeling are relatively large and cost money. The best that can be done on the lowest end is to drone out in a narrow low end band so every low frequency sounds pretty much the same. As for which soundbar to go for I would suggest to find a store that demo’s them and trust your ears.
The following how-to can also be used for a point of reference for many audio related questions…