i have a 2 year old 1st edition Dell Studio 1535, bought from the US,
2.OG intel
256 ATI mobility 3400 (max res 14xx x 9xx)
3G ram
about 100G hdd

i can run SC2 at full res at low details, smoothly on OFFLINE (campaign) play but lags on ONLINE

and overheats and shuts my lappy down after about 2hrs play

for OFFLINE players you might to consider your video settings to be at least 1G for hi-res play or at least setup for HD.

you might want to have a good cooler as even the high end ones are having issues when playing SC2 at hi-res if the cooling system isnt good. (my friend is using M15x at 1G video, but had a crappy cooler, it overheats and shuts down after 2-3 hour gameplay of SC2

for ONLINE players, better recheck you connectivity, broadband or cable AND your video and cooling system.

recommended settings for hi-res play (botth online and offline) for continious play

at least
2.0G cpu
3G ram
1G video
1Mbps connection
about 20G free hdd
very nice cooling system

i didnt name any brand as so long as the brand meets the requirements, SC2 would run OK

OR you can always check SC2 official website for details