It definitely depends on the individual place. Some provide hutches, some don't - and of course if you already had a decent sized/condition hutch, I'm sure most rescues wouldn't insist on you using one of theirs! I bought my own hutches when I started fostering a few years ago, but that was more down to my choice than anything else - of course it helps the rescue but also it gave me a little more flexibility to use them for my own buns or to rescue one on my own.
I would normally pay for everyday goods such as food, hay, litter etc, and the rescue would pay for vets bills - or at least they should 'technically' be responsible for them but as far as possible I try and pay myself. I appreciate that not everyone can help in that way though, so as long as the situation is made clear at the outset, it shouldn't be a problem. You may have to bear in mind though that emergencies do arise from time to time, and you may end up having to be able to find money for emergency vet fees before the rescue can reimburse them (e.g. if you have to rush somewhere in the middle of the night for treatment). You will also need to be able to get to a vet whenever is necessary, and this includes for emergencies.
Also, you'd need to have a dialogue with the rescue you're working with as to why they want fosterers. If it's a rescue mainly based at one premises, they would probably want all of the 'ready for rehoming' ones there, so that potential adopters can see all those that are ready. So this can mean that fosterers are used to provide temporary emergency care (e.g. if there is an urgent case but nowhere to put it!), for poorly buns if the fosterer is able to cope with this, for buns that have behavioural problems that need work (my favourite!) or for buns that need to gain/lose weight before they can be neutered. If a rescue is based on a network of fosterers then of course you may just have normal bunnies waiting for rehoming - although this may also mean that you'd be expected to have visitors come to view the bunnies.
Just as a general note, you will also need to make sure that your foster area is totally separated from your own bunnies - you need to be very careful about the potential for the spread of infectious diseases, especially with newly "admitted" buns with no known history, and sometimes the smell/sight of new bunnies can cause fights among bonded couples, so it's important that they are separate and dealt with at separate times. If you're handling them a lot I'd also suggest changing jumper etc again to help with preventing cross-contamination and taking smells around the other buns.
There are a lot of variables, so the best thing you can do is find a rescue near you and offer to help, and see what they say. Not every rescue will use fosterers, or will use them in a different way to how you are able to help, so it's really a case of having a chat with some and see what happens.