It’s good to establish trust first,, but I too wouldn’t forgo needed care first if nails were too long etc., and whereever you get your rabbits from, you should ask them to show you how to trim their nails and clean their anal glands. That way, it’s all done prior and you can do all the bonding/gain trust stuff for the next month.
I also think it is a good idea to get a check-up right away with a rabbit-savvy vet (very important!) anyway, and they can also show you how to do these things.
I want to address your concerns about anal gland cleaning – I am thinking you are thinking you need to clean their anus, as you said how far up do you have to go. What you are actually doing is cleaning the glands ONLY. Which are little slits on either side of the genitalia mound. The slits are like little pockets, that are somewhat shallow – no “far up” stuff. Inside, it collects this waxy stuff that can get hard, uncomfortable and can even cause infection. Some bunnies produce more waxy stuff than others, and so with regular maintenance of just “checking” you will be able to find out how often you should actually clean them.