Bass is a good instrument to start on because it's not too hard to get to a basic but decent, ready to mess around in a band standard fairly quickly. This is because you've only got four strings to think about and you generally only have to play them one at a time. Some bass players do use five (or more) string basses, which might be of interest to you, but Clayton doesn't, and some, including Clayton, do play chords (a chord means more than one string at a time) but most of the time not, and in fact Adam very rarely does these days. U2 songs aren't terribly difficult to play by and large, Adam belongs to the school of solid and tasteful playing rather than the twiddly fingers brigade, so the bass parts should be manageable for bass players of almost any standard, though I would suggest listening to/learning from other players too, Clayton is a good bass player and all but someone like (for example) Tony Levin is in a different league to just about any bass player you care to name. Having said all that, any instrument is impossible if you don't really work at it. Be prepared to put in a lot of hours practicing songs over and over again until they become automatic. Fingering technique for both hands is really important too, so I would suggest that a good teacher is worth every penny, but if you can't afford that then get one of the instructional videos to study or get a friend to help you out. The main thing (IMO) is to learn to "feel" and stay with the beat of the music in your head; the most important part of a bass players job is, together with the drummer, to keep the band in solid time. If you can do that then you're 50% of the way there IMO.
What bass to buy? My own preference has always been towards Fenders and Fender styled instruments. It's a classic, popular styling, always in fashion, looks good for any style of music, and easier than many other instruments to sell/part exchange if you decide to trade up to a better bass after a year or two. Personally I'd recommend a Jazz bass because of the thinner neck which for beginners is much easier to play than that found on a Precision bass (Adam plays both of these models by the way). Fender do a budget line (called Squier) which aren't bad for the money (around $250 US new) or you can pick up a second hand made in Mexico Fender bass for around that. Or you can spend less and get a non-Fender copy, again, quality varies from manufacturer to manufacturer so watch out, and resale or trade in value may be slight or nil. I'd suggest a yellow/red/black sunburst or other classic finish (e.g. gloss black etc.) for the sole reason that they are easier to sell if you want to get rid of it at some point. Personally I'd recommend a Tokai Jazz copy, they look like 60's Fenders, play very well and often cost less than a new genuine budget Fender. I have two Tokai basses and love them both. If you have a choice get one made before 1985 since they are *exact* replicas of the early Fender models (in fact Fender sued them over it, such was their accuracy). ebay is a good place to browse for basses actually, there's lots there so see what models take your fancy. I've bought a few instruments there actually. Other brands used by starters are Yamaha, MTD, Epiphone etc. etc. If possible I'd go to a store with a friend who knows something about bass and fiddle about with a few and see how you get on.
Hope this helps, let us know how you get on.
Mick