The other posters are correct, goats tend to browse and sheep tend to graze.... BUT goats will eat pasture and sheep will eat browse. If you never ever want to mow, sheep may be a better choice.
I would have to strongly disagree with that the idea that goats are harder to fence. Let me tell you from experience, this is NOT TRUE! I have dealt with many many goats, never had a problem of them getting out. The sheep? They were getting out constantly! You have no idea how many time I had to rescue them off the road
Another member who isn't on here very often anymore said the same thing. If I remember right she had ~60 sheep? and a few goats. Goats never got out but again the sheep were always trying to get out. I know other folks that say the same thing.
I have found that goats can be made into more of a "pet" then sheep. I know there are friendly sheep out there, but those seem to be few and far between.
Wethers are great starter goats, but many progress over a short time from wanting lawn mowers to wanting to breed once or twice and try milking. Unless you are absolutely sure that you never ever want to breed or milk, I'd get at least one doe. You will then have the option of breeding or milking without having to add in more does at a later time. If you have children, consider if they would be interested in showing at some of the fairs etc.
Just a tip, be cautious when buying from folks who call does/bucks "billies" & "nannies". In the goat world, this is more of a negative term. Folks who say billy/nanny are generally uneducated when it comes to goats and aren't able to mentor new goat owners. Not trying to be mean, just something I've noticed. Doesn't mean ALL people are like this...