As you are in the UK, your music is automatically copyrighted. I would still recommend registering your copyright with the US copyright office in case you ever have to defend that copyright in the US (it is the biggest, single copyright zone, so well worth doing especially if the result will be on the internet. If money is an issue, you don't absolutely need to register right away but it is advised that you do it soon (I have a funny feeling it has to be within a set period (18 months springs to my mind, but I am not sure off the top of my head) . Posting files may help in the UK in terms of establishing copyright, but in the US to qualify I believe a transaction needs to occur to qualify as published, and to be defensible in the US courts it really HAS to be registered.
Fee wise, certainly no fee is not uncommon, though a stipulation of accreditation for the music as part of the video and in any accreditation when the video is posted anywhere would certainly be expected...
Why not sound them out on a nominal fee of $35 (the cost of copyright registration), plus recommending that they also register the video with the US copyright office? Fees really come down to a balancing act between how much they want your song, versus how much you want your music to be used. If it's not a commercial video release (which a show reel isn't) then perhaps a nominal fee is the better idea. You don't need to register a copyright for every single derived edit of your song, only if it is what would be understood to be a separate work.
Copyright permission wise, you need to set the permissions for use. ie what zones, how long, and what exact permissions (worldwide or not, exclusive or not, derived works, distribution, redistribution, revokable or not, assignable or not etc). Incidently, you can stipulate that if the video is ever used or distributed commercially (ie money is received by them for use of the video in any form) then you would be due a percentage of any monies received. That way if they are ever paid, so are you, while at the same time they are not being charged a huge fixed cost while at the same time having no income from the video. In your contract you can also make your fee contingent on them performing certain promotion tasks. You might want, for example, to encourage them to do something with the video (post on YouTube or vimeo, promotion posts, a press release etc). You might also want to stipulate that YOU can use the resulting work in promotion of your music, with a set of complimentary permissions set by them. For example, that you can use the work and create derived works (ie edit) without cost, worldwide,irrevocable etc.