Quick Carpeting question
Baseboard should be installed first. Down on the floor or slightly raised makes no difference. If you install after and ever need a restretch or repair or replace, all the base would need to be pulled again.
For instance, if the floor would ever flood, the base would need to be pulled to dry the carpet, if installed on top of the carpet.
Also, it is better to stretch off baseboard than drywall.
"I'm twisted, not sick. Sick implies, I'll get better"
Installing since 1973