Hello:
I am not going to offer up a specific model, per se, since those change so often, that a model I say has done me good may already be unavailable. However, I will share some experiences I've had with different brands in the desktop replacement arena:
Toshiba: Overall, I have had the best experience with these. I've used three myself (use one for my small consulting stuff), and have supported/deployed about 40 overall. I can't give any information as to how their support responds, because I've never needed it.
IBM: Good experiences overall with IBM. The issues I have had are with the batteries dying (and I don't mean needing calibration...I mean bad battery) and intermittent wireless issues (was resolved with a BIOS update). I've used 2 myself and rolled out about 100. Their support needed a little push, but wasn't too bad overall.
HP/COMPAQ: Average experience overall. Some models have performed really well, others have been clunkers. I'd say stay away from an initial model offering (HXP 7000) and wait for an updated model (HXP 7020..btw...not even sure these are real models...using for illustrative purposes only); since they seem to be a little buggy starting off. Their support is also pretty hit or miss (one guy will ask whether or not you've rebooted, the next guy will actually tell you there is a BIOS revision to address the issue right off the bat). I've had probably 5 of these (using one now, as it is my company's standard), and rolled out 200 or so personally.
Dell: Ditto just about everything I just wrote about HP/CPQ. Have used a lot less, though...2 personally and rolled out 20 or so.
I think the latest reviews by Concumer Reports stated that Toshibas and IBMS were well ahead of the pack in terms of major issues/repairs, as well. But these were a few months ago...so you may want to look at CNET or something for a more up-to-date review of model-by-repair frequency.
I've used some other brands (Sony, Gateway), but those were just for portability, and not for the desktop replacements; so I won't offer commentary.
Again, this has only been my experience; others may have had better/worse luck with the same brands.
Good luck!