Any 7/8/9 Speed derailleur with enough capacity (essentially cage length) will work.
Shifting quality is about the system, not a single component. Replacing just the derailleur, even with the very best, will make little difference. However reasonable quality components are often available at discount prices cheaper than low spec components, so shop around for the best quality derailleur that fits you price point, but see below.... While other brands (SRAM and Microshift) make compatible components, its probably best to stay with with Shimano.
Without knowing more about the bike, here is the order I would be looking at things to improve shifting.
New, quality cables (inner and outer) would be my likely make more difference than the shifter. Unless the existing cables are 'as new' these would be my first thing to change and would always go with a new derailleur.
Chain and cassette - these wear out and need replacing occasionally anyway. If worn, they will cause bad shifting.
Shifter - while the feel of shifting is affected by having a quality shifter, its probably at the bottom of the list of things that cause poor shifting.
With all the above done, tuning can make or break the setup. Be prepared to spend time getting it right.