From working for 2 guitar makers -
Many companies have differing levels of relationship you can enter into -
Low level endorsers will get things for trade is generally the rule of thumb, these people will be hard working, heavy touring musicians who can get the brand exposure and will benefit from not paying full whack for strings etc when on the road. Often instruments and amps can be loaned out as well to an artist for a predetermined time, a tour, a recording, a TV appearence etc. You might be asked in return to play on trade show booths, demo videos, in stores etc.
Next up will be a discounted trade deal, so they will buy for even less, sometimes at this level the sundry products become free, so you pay a little less for a bass and the strings are now free. It all gets more complex if you endorse more than one company (one for strings, one for amps, one for guitars etc etc) but you often get a few more freebies. At this level you are likely to be taken advantage of a little more in terms of being asked to play at events etc. At this level you might get special treatment as well, reserve wood stocks and prototype things to try out which are not available to the public.
Then you have your 'established musicians' they wont pay for stuff at all and be asked a lot to demo product for videos, turn up for signing events etc and be used more often in brand advertising. Many people at this level have several companies they endorse. Sometimes to keep everything on the books you will pay a token fee (£1 or so) for everything you have.
Above them are your household names, they will get the big ad's, the custom instruments, the works. In an ideal world the brand get them to turn out to a trade show or two but simply having the name is enough.
Artists with signature models get paid royalties based on the sale of the instrument or whatever in many cases.