Thank god that my hand shakiness is not that bad that I see 'shaky' images thru my viewfinder and 'hoping' to get a good shot. The image stabliser in my cam body has served me well enough and so far I managed to get shots of sunset without a tripod.
Minolta. Konica Minolta. Sony
Erm... in the first place, you want a "easy to use (point and shoot kind)" for "occassional events". Thus is it wise to jump onto the (D)SLR wagon? Especially considering that you're jumping direct from a P&S. Do note that mastering the use of SLR to produce "beautiful pictures" will take time and effort, something which I don't feel coming from your post (or maybe I'm just too dense to feel it. ).
So my little advice is to think it through, whether it's worthwhile to be spending the money on a SLR (since you mentioned you're on a tight budget), or get a new P&S/Prosumer instead.
If you're still convinced on getting a SLR, there's plenty of advice to go around here on CS.