Re: If you had $1000 to... What do you have the most of where you live, sun, wind, or spare vegetation?
Re: If you had $1000 to... Equal amounts of all of them, relatively speaking. There is not one that is more apparent than the other. Or put in a better way - you could take the generator anywhere you want that inhabits people, except for "extreme" locations.
Re: If you had $1000 to... In that case, I suppose the best bet is a methane digester because it would be the least intermittent.
Re: If you had $1000 to... $1000 isn't that much. A quick google tells me I'd be lucky to get a 1kw solar panel in the UK with that.
Re: If you had $1000 to... Yes it's not a lot, but solar panels are very expensive. Wouldn't hydroelectric energy also be much easier to develop and not intermittent if near a body of water.
Pretty open ended question a REAL answer would be influenced by many factors, As stated - I would go solar with battery storage, low maintenance simple device - etc. Then just use the DC and/or small inverter to power AC items directly. Developing a complete digester system or hydro for $1000 - would be a challenge.
I could do it for that cost. I'd wait until hurricane season is over, and buy a generator cheap on eBay. New never used, unless we actually get hit by a hurricane. Look for a dual fuel model, using gasoline or propane. Then change out the propane orifice out to burn methane. Put an alcohol kit into it. Now you can run on either alcohol or methane. But be careful of the swamp gas. It has lots of stuff in it that are not good for the engine.