Here are some ways to make owning a rabbit less expensive.
When first getting a rabbit think about the size. If you really want to spend as little as possible, you might want to get a small breed rabbit. Larger breeds require more expensive housing and lots of food. But, make sure to still take their personalities into account. Small breeds tend to be more active while large breeds are calmer. Generally.
Rescue a bunny from a shelter or rabbit rescue. Shelters and rescues are much cheaper than pet stores, and rabbit rescues have often already spayed/neutered their rabbits. So you won't have to spend a big chunk of change if you want that done.
Don't house your rabbit outdoors. Housing a rabbit outdoors requires a hutch and a hutch requires a lot more maintenance than an indoor cage. Hutches are also very expensive. Proper sized hutches cost around 250 to 350 dollars. If you are housing your rabbit indoors you can rabbit proof a room for your rabbit which is the cheapest option. If they are chewers however, you may save more money by investing in a cage. The cheapest option is to build your own cage using wire shelving grids and zip ties. If you build your own cage, I would suggest researching it online first. Some very good cages for your rabbit can simply be a small animal pen. You can buy small pet pens for 40 dollars at most pet stores that are a good size for most small and medium sized rabbits. You can buy expansion grids for larger breeds.
If you want to save money, definitely get your rabbit litter box trained. This way you do not have to worry about having a cage bottom like the ones on store bought cages. You also will not have to cover the bottom of the cage with litter, only the litter box.
All rabbits love and need toys to keep them entertained but you don't have to spend a fortune. Home made toys are a good way to go. Cardboard tubes and boxes are favorites of bunnies. Just make sure to use cardboard without ink on it. Plastic baby toys, cat toys (only plastic ones and no catnip!), or toys meant for small pets are all good. Plastic toys last a long time for a rabbit and are easy to clean. Don't go crazy buying wood toys or hay toys. By a few once in a while. They get destroyed easily. Just make sure your rabbit always has some kind of chew toy. You can even use a piece of untreated wood if you want to really save money.
Don't waste your money on cage cleaners found in pet stores. A vinegar and water solution works better and is much cheaper. You can use the vinegar solution to clean the litter box and the cage. Just make sure to rinse it off very well, because some rabbits dislike the smell. For food and water dishes, a very small amount of dish soap and hot water are a good way to clean them. Just make sure to thoroughly rinse.
Rabbits all like a comfy place to sleep, but they don't require a fancy bed or anything. Most rabbits are very happy with some towels. You can find large bath towels for around five dollars instead of a bed which would cost around 15 dollars +. Rabbits love towels because they can play with them and arrange them however they want. And you will be happy because they are easy to clean, just throw the towels in the washing machine.
When buying food and water dishes don't be fooled. Yes, plastic ones can be very, very, very cheap. They can cost as little as a dollar. But, they might end up costing more in the long run. The cheap plastic dishes are not very durable. A heavy duty ceramic bowl is a better long lasting option that only costs a few dollars more.
For grooming supplies a brush and nail clippers are needed but don't invest in shampoo unless your rabbit actually needs it. Most rabbits are very clean animals and my never even need a bath.
For hay look for a good quality hay, but you can try to get the cheapest you can find, as long as the quality is still good. A good brand is Kaytee. It is on the cheaper side, yet the quality is pretty good, and I find that most hay-eating critters really love it. Be careful of the extremely inexepensive brands such as Great Choice and brands that advertise easy to use miniature bales separated into portions. Those brand's hay is horrible quality and most rabbits won't eat it so don't waste your money on it.
You can find many good quality pellets for fairly inexpensive, but make sure not to go for the super cheap stuff filled with seeds and other stuff. That is not healthy for your rabbit. Also make sure that Timothy Hay is the first ingredient.
To save on veggies you can try growing your own. You can use something such as romaine lettuce as the main part of your rabbit's daily salad. And then you can add more expensive veggies such as parsley, cucuumbers etc in smaller amounts. Celery too.
When you are in the pet store shopping for your rabbit you might see vitamins for them. Don't buy them. They are fairly expensive and they are completely unnecessary. If your rabbit gets hay, a good quality pellet food, and a variety of veggies he will not need any extra vitamins.