My wife's bike is equipped similarly and everything shifts fine on it. Don't worry about it until you've at least tried it.
As for anything below Deore = crap, that just isn't true. I would say that current alivio/altus is better than older Deore, and we didn't think it was crap back then. Shimano does a pretty good job of trickling down their improvements to the lower end, and keeps the latest in the higher end.
And it isn't true that upgrading to Deore will require all new parts. The entire line of products is compatible as long as you have the same # of gears, with the exception of 10sp MTB <> 10sp Road. So if you replace you 9sp derailleur with another higher model 9sp you'll be fine with the shifters. Dura Ace has a few exceptions too, but you're not going to DA, it'll cost more than the bike. 10sp MTB uses a newer system called DynaSys, and the cable pull ratio is different than all the others, so it won't work with anything else. But the cog spacing is the same, the chains are compatible even thought the DynaSys chains supposedly work better, and the front is even compatible to a degree.