Assuming you're coming in from the US, then, yes, customs will be after baggage reclaim. This isn't a lengthy process in the UK - you'll probably walk straight through without seeing anyone (they tend to watch through cameras or two-way mirrors). You will have gone through immigration before baggage reclaim, of course.

There are, as mentioned above, free luggage trolleys around (tons of them, in fact). If these are too small, there are 'official' porters in the baggage hall, who charge £7 for a 'normal' amount of luggage.