Your costs will depend on exactly what you want to do, and how advanced you want to make things.
So, how much film do you want to process? How often? And the most important question is do you want to print your stuff in a dark room yourself, or develop and scan, or send your processed negatives out?
A basic daylight developing tank is generally a very inexpensive way to go about doing things, especially if you aren't jumping into sheet development right away. You don't need a 'darkroom', just a simple 'dark space' that can be as small as a changing bag for when you transfer the film into the daylight tank, and then everything else can be done at a laundry sink or even a table somewhere with a few buckets. (I don't really support film processing near food prep or eating areas if it can be avoided.)
Costs of course go up as you add more in, but these days equipment can be had for very cheap if you're willing to wait and deal with potential issues of used gear. But if you are going to get into building a darkroom space, then I strongly encourage careful planning for air exchange, electrical, and the plumbing. Not something to rush.