Microsoft Security Essentials contains antivirus and as such should not be used together with McAfee products. It could feasibly open up your machine to infection due to the two antivirus components clashing.
Windows Defender (standalone) can be used as it is simply antispyware but it will be disabled by McAfee when the latter is first installed. It's OK to re-enable it afterwards and use it.
It is already included in Vista and Windows 7 and is an optional download for XP.
McAFee is fully compatible with XP SP3 x86 (32-bit version only) and Windows 7 SP1 x86 or x64 (32 and 64-bit) as long as you keep them totally up to date there should be no problems.
BSOD's and the problems you say you were having indicate to me that something wasn't up to date, most likely drivers and McAfee simply was the catalyst for a breakdown that was most likely inevitable, also it could be due to lack of resources (memory or RAM, free hard drive space etc.). There is always Technical Support Online Chat available for help in that regard.
(Useful Links above).
Another factor that can cause problems is the overuse of registry cleaners, or, of course, infection.