Best to ask the retailer what it comes with, some companies sell fitting kits separately so you can fit one computer to multiple bikes, my Cateye comes with the option to configure two bikes in to it for just this reason although the interface is so fiddly I can't imagine me ever doing it no matter how tempting, others might sell extra bits that you consider 'required'.
Watch with wireless and cadence that the cadence sensor is also wireless. I use a Cateye strada with cadence that is all wireless, but I think it was a tenner or so above your budget (may be deals around though) I think sometimes computers can be sold 'cadence ready' but the sensor kit is extra too, be wary of that. The original Cateye my LBS tried to sell me was wireless speed, but wired cadence and being sold as 'wireless' because of the speed connection.
I'm comfortably at the novice end of things and I like having the cadence sensor on my 'bike to do sportive training and the like on'. Basically it keeps me honest and if I want to try to ride to cadence, which I sometimes do, it's the only way I'm going to be able to and know that it's happening. I care about it a lot more than speed as an indication of how I'm doing and use it a bit like a rev counter on when to change up or down through the gears. My commuter doesn't have cadence on the bike computer and I don't miss it, but I find myself looking at the clock more than any other readout on it lately. I believe my cadence has increased on the commuter through practice on the road bike.
It's probably a phase you need to go through at some point, especially if you want to get faster (much like shouting at ignorant car drivers is a commuting phase, now I just smile and wave.)
They are pretty bullet proof (my cat eye has bounced down the road more than once as the mount could be better designed) and there are no moving parts, so on your budget a used one might be the way to go, just make sure they are selling it with all the bits.