No experience with paid work yet, but for sysadmin work I'd mostly look at the environment and how the previous admin left the premises, and why they left. I wouldn't want to work with a bird's nest for a server room, that's got everything jammed into one clusterfuck of a god-function sort of server or something crazy like that. Separation of services, security, wire management, all those things matter because that's the state that you'll be working in, and cleaning up someone else's mess.. it makes my blood boil.

Payment is important, and if the job doesn't pay well, don't take it. Or if they place a wee bit too much value in those expensive pieces of toilet paper called certificates, it denotes incompetence from the employer by being unable to gauge your skills on their own (and I get that there's time management involved, but come on.. how long can it take to have a conversation with someone to gauge what their skillset is). But the working environment in particular is of vital importance. If it's all going to be yours to build, great (and don't you dare to half-ass it -_-). But if it's already been partially done by someone else, they'd better done it well.