cheap or expensive?

what should I choose?

always cheap if you can't afford it, always expensive if you can afford it. But what does your question refers to??

If this is for a domain name that you plan to make a site on, then I'd suggest going for cheap. With expensive, you don't know if you'll get your money back on the domain name when you sell it - there's such a lot of risk. Things that sound like they'll be a certain bet are often not!

The only exception is a 4 letter .com, they tend to hold value reliably and you won't have trouble selling it again. Then again, 4 letter .com's tend to be a random jumble of letters (except the ones that make actual words and most of those are not for sale right now and if they are, it's $$$$$). So I would not recommend a 4 letter .com in terms of branding purposes, although in terms of holding its value predictably it's better than other domains where they can go up and down a lot.

I've always built my sites on cheap domains - some were expired cheap domains, others were ones I hand-registered. My take-home message is: if you're building a site, content > domain name value.

But without knowing what you're planning on doing with the domain name, I can't tailor my advice to your situation. If you want to use it for a 301 redirect, for example, then DR and backlinks of the domain are going to be your most important metric (well, you also need to look at the domain name itself just to be sure you don't have a branding mismatch).

OP: Are your asking about new domain name registration?
Which extension?