For my stealth-oriented thief/archer/assassin character, I find Lydia to be an invaluable asset in easily 80-90% of circumstances. It does take care, though -- she's noisy, especially in the upgraded armor I've given her and carrying that big, heavy, two-handed axe I gave her, so for spots where I want to sneak on ahead and quietly take things out, I tell her to wait, then come back and get her when it's time to move forward again. And, yes, I sometimes do have to tell her to just wait for me while I solo a particularly tricky area that requires absolute stealth -- like most Thieves' Guild quests, for example.
What makes her truly invaluable though is having the closest equivalent of a Sherman tank to back me up when stuff invariably hits the fan. She's proven a capable dragonslayer (although her giant-slaying skills mostly amount to method acting a hacky-sack...), and even when I've told her to wait somewhere she'll come sprinting forward to cover my back if I screw up and find myself having bitten off more than I can chew!
All this said, try out different companions until you find one that you like and that works for you, or decide you're better off just going solo. So far I've used only Lydia, but Aela and Jenassa seem like they'd be good fits for a stealth-oriented character, the former however requiring you to complete a somewhat lengthy quest chain, whereas the latter just wants 500 gold; I'll probably give each of them a trial and see then if I still like Lydia.