What lens mount adapter do I need for nikkor 1.4 ai-s to be mounted on 550d?

Do I need a ai adapter or ai-s adapter? The prices are different by a big gap

Added (1). I want to focus to infinity by the way, the lens will and some adapter I saw say that is possible with this adapter.

Ai adapter I think

Note that any adaptor to use any Nikon lens on any Canon will most likely not carry all the functions of the lens to the camera body. Best to try in a good camera shop, then you can see if the combination will do what you want, and not damage camera or lens. Nikon and Canon come from very different design philosophies so in my mind it would be lucky if you got any reasonable functioning from such a combination. It's like trying to fit a Ford engine into a General Motors car.

The other thing is - does the combination focus back to infinity, or would it be for close-up use only?

All Nikon-F to Canon EF adapters will focus to infinity, unless it's extremely badly made. Any Nikon F-mount adapter will work and give you stop down metering. Novoflex do additionally make a AI/AI-S smart adapter which gives you open aperture metering (via AI-coupling ridge) and operates the coupling prong in the lens for automatic stop down, (i.e.giving you full AI functionality), however this costs £150.