That's hard to determine. I wouldn't try building a skimmer to start with. That's a pretty advanced experiment, and it wouldn't be cool to spend the money on the materials and end up with a piece of junk. Where do you live? Maybe there is a local marine aquarium society? If you live in or near a large city there probably is, and if so, you can usually buy used equipment from members for pretty cheap. Plus, they could help you figure out how to set it up, and how to maintain your water.
A good protein skimmer might run you anywhere from $100 up to $300, even more for some of the real fancy skimmer/sump combos. As far as a tank goes, you should try to find one that's pre-drilled... or set up for a sump. This will let you put all of the extra equipment in the sump, and not in the display tank. One of the pains of having a regular aquarium, is that you have to seal all of your equipment so it doesn't get sucked in or escape through cracks between your equipment and lids. With a sump, you only have to worry about the intake being screened off, which is pretty easy. Then again, you have to plumb the sump to the tank, buy a good pump to return water back to the tank from the sump.... oh man. Yeah, you need to do lots of reading!
As an example though, I bought a pre-drilled 72 gallon bowfront tank, with stand, canopy, lids, and completely ready sump with all the plumbing, and with a protein skimmer, for $500 cash from a local aquarium society member. It's everything I would need for an octopus, minus lighting, and lighting is really cheap considering you don't need anything fancy, just low-wattage fluorescents.
You say you are getting a seahorse tank?