For just starting out, I suggest reading up on oilstones, waterstones, diamond and scary sharp (sandpaper). They all do the job.
For power sharpening, I think a 1x30 strip sander is the best bang for the buck. Plus you can get belts up to leather for honing.
Pick one method that you find meets your needs. For example, if you have an unheated shop, wet waterstones may freeze and crack (not fun, as I found out). But if you don't mind bringing them indoors, not so big a factor.
Sandpaper sounds cheap, but quickly rivals the cost of a stone in a surprisingly short time.
There are lots of inexpensive stones to look at.
For carving, you could also get away with smaller stones as you don't need the surface area for something like a plane iron.
Every system has a coarse, medium, fine option. While you can go super fine with stones, it can be needlessly expensive this early in your carving career. Also you don't need every stone from coarse up to super fine.
Honing compounds are inexpensive and can be used on everything from cardboard to leather belts to scrap wood. Only a few dollars here, but worth a million.
When you pick a system, my best advice is to stick with it. Don't get bogged down in oil vs water or mix and matching. That creates distractions early on that will just confuse you.
In short order you will figure out what you like and then can refine or explore other options.
I think you can't do better than The Perfect Edge book from Ron Hock.
Hope that helps.
Jim