.cheap domains

How easy is it to rank for a low comp, one word niche keyword using a niche.cheap domain? My main keyword would be 'Cheap [Niche]'?

I don't think it would be anymore difficult than ranking the COM, NET, BIZ, or INFO extension. Google doesn't discriminate about what extension you're using. There are so many other metrics that play a role, don't worry about the extension (unless it's a ccTLD like .DE/.IN/.EU..etc)

Yup, gTLD's are not penalized. ccTLD's like "Mixing" mentioned might bring bad rankings on Google.cooom but might work better on national Google pages.

Google says the TLD doesn't matter most of the times. I have got a few .tv domains (considered by Google as gTLD) and they rank OK. But I can't say the same thing for .cheap tld. Google has a list of domains which it considers as gTLDs. It's always better to choose a gTLD if you are targetting all locations. Below is the list of domains that Google considers as gTLDs.
https://support.google.com/webmasters/answer/1347922?hl=en