A separate structure will require power and HVAC and unless you fancy running through the cold when you need to pee it'll require plumbing too.
It's a farm. I'll just open the door and go. (kidding)
I do have the option to hook another bathroom to our septic system, but I'm not too worried about it. It would be about a 60-second walk back to the house, and while it's always raining in the northwest, it's usually only below freezing for a few weeks out of the year. Maybe I'll get an umbrella.
HVAC is a tricky beast. You have to control both temperature and humidity. You can hack together temperature control with cheap window units but if you want humidity control so you're not wet in the summer and sick (because of the dryness) in the winter you'll need real (expensive) HVAC.
I'm one of those people that rarely gets cold. As a kid I regularly wore sandals during the winter. Heat on the other hand sucks. Anything above ~65ish and I'm miserable. I figure the small collection of servers would be enough to keep it warm. They are currently in a closet off the bedroom, and the bedroom is currently ~65ish while it's ~30 outside.
Power is a fiddly beast too. You're not just running an outlet here, you're feeding a subpanel.
You're not erecting a shed here. You're in to at least a few tens of thousands of dollars.
Anything over 12v DC and I get nervous. I'm basically capable of replacing a 110 outlet or a light fixture, but I've been nailed a few times by what my electrician called a 'shared neutral' (I could be mis-remembering. No power to the outlet because I turned the breaker off, then my wife flipped a switch in another room and I got nailed. The 3-light power tester thing still said the outlet was dead). Regardless, I'll have an electrician hook all that up. I'd rather pay for it in cash than pay for it with my life. ;)
Just how generous is your new employer?
Surprisingly. I told them my target wage. They asked "why so low". I replied that they were taking a risk on hiring me--especially for a remote position, but that I knew my stuff and would bring in a lot of money during my 6-month 'probation'. I told them once probation was over I would re-negotiate. When they sent over their offer, it was nearly double.