They will take photos of you ( digitals / Polaroids) and maybe a walking video.
In terms of signing, it would depend on how big/ small the agency is and location.
Getting signed shouldn’t be what you thinking about now. It’s more about what you want out of this collaboration.
Sometimes signing with an agency does more harm to you than good because this means you exclusively belong to them and cannot freelance.
If it’s a local agency that does mostly catalogs, some mall catwalk shows, some short films or commercials here and there, you do not need to be signed to work with them. You can sign a non exclusive contract which means that will contact you for jobs, but you are able to look for your own jobs elsewhere.
My experiences involved going to as many local agencies I could for non exclusive collaboration and I got many more jobs this way than signing with one agency ( which I had done before as well ).
If it’s a very big, prominent agency like ELITE, IMG, FORD, then exclusive is the way to go because they would have much more quality jobs that small agencies can’t get such as a spread in Vogue , advertisement for Burberry or catalog for ZARA. Usually their clients are well known or are reputable and not small businesses. There’s more of a career and growth prospect with a big , reputable agency like that. Competition is big too and some models are signed and probably don’t get any jobs a year. Again, signing does not mean you will get jobs. They could send you to castings and you are never picked.
So again, is this just a side job or do you want it to lead somewhere? Think about these before jumping into contracts.