I'm not too Nikon-knowledgeable, but it might be roughly the equivalent of the Nikon FE: manual focus, shutter-priority autoexposure (contra the Nikon's aperture priority), respectable-quality center-weighted meter, robust but not really built for "professional" abuse by the standards of the day. A lot of people feel that Nikkor lenses are a touch better than their Canon equivalents, but a lot of people also will dispute it---certainly a lot of the Canon FD glass is very good any way you look at it, and FD lenses are cheaper than comparable Nikkors because they won't work on modern bodies (Canon abandoned the FD mount when it launched the EOS autofocus line).
There were a LOT of AE-1s sold; in the US, everybody's dad in the 1970s had one for taking family vacation photos. Most of them came with the 50/1.8, which is a good general-purpose lens not unlike, well, the Nikkor manual-focus 50/1.8; the 28/2.8 was the usual second lens and also has a good reputation as far as I know. You don't have to do the Nikon lens-registration routine with the aperture ring. Everybody has their own taste and preferences, but to me the AE-1 seems like a really convenient body; it sort of gets out of your way and just does its job with no drama.
The only significant common problem I can think of is the shutter squeal, which you'll hear if it's there---I assume you've already dry-fired the camera and you didn't mention any horrible noises, so you're probably OK on that front. If the battery is OK, the meter should be fine; it's a center-weighted incident meter, so it'll have the limitations inherent to that design.
There are some very good FD lenses (both Canon and third-party), but the kit you've got is more than adequate for practical use, apart from the absence of a telephoto. I'm not sure you need to wait for spring---it's a nice fast lens; just drop some Tri-X in and do a test roll of winter street shooting to make sure things are in working order.