A lot depends on your usage, and of course your budget. Assuming your bike is 9 speed triple, you have a choice of Alivio, Acera, Deore, SLX or Deore XT. They improve in performance and construction a s you progress upwards, but 9 speed Deore, SLX or XT will be harder to find new, most having gone to 10 speed in the last couple of years. That said, if you can find them in 9 speed new, they may be dearer than 10 speed through supply and demand.
I am surprised however that your shifters need changing. The internals don't usually corrode, although the cable might have done, hence the initial reluctance to shift/engage. That's most likely to be sticky or corroded cables (inner and outer) than the shifters.
Bestest by far, and of course most expensive option would be to upgrade the lot to 10 speed, as you'll benefit from a new cassette and chain, but of course that will seriously dent your wallet.
Next, search the websites for 9 speed shifters. Look at
Chain Reaction,
Ribble, Planet X, Merlin,
Evans and
Wiggle, Woollyhatshop, and (shudders) Tweeks,
Cyclestore,
Rutland Cycling. They would be my go-to searches, and my purchase choice depends on Price, delivery and Quidco rates. If you do buy shifters, they usually come with inner cables already. Then you'll need some outer of the right length. A lot of
eBay sellers will sell you outer by the meter and include ferrules and end caps. Treat yourself to a decent pair of cable cutters......a lifetime investment you will never regret.
Next, scour classifieds on Singletrackworld and Pinkbike for used shifters from someone upgrading to 10 speed. Loads of bargains to be had. Cables from eBay or wherever will not cost huge money.
Final option, just replace the cables. It may solve the problem altogether, for about a tenner if you shop round.
Have fun
