I have one of each kind of sharpening system. This will get as good a job done as anything.
Woodcraft puts these on sale a couple of times a year for 25 bucks.
This is a large fraction of your budget, but well worth the 68.50 at taking the skill out of getting a perfect edge. I have one, as well as an original Eclipse, and a Record with a little ball for a pivot point, so I'm not just pulling this out of the air. http://www.leevalley.com/US/wood/Pag...72,43078,51868
Get one each of these when you order the MkII. Get the plain. With the surface plate, it has the perfect texture on the surface that all you have to do is put a splash of water on the plate, and this paper will stay in place. Don't get heavy handed with it to start with. Also get some various grits of Wet-or-dry sandpaper to use for coarser grits from your local hardware store. http://www.leevalley.com/us/wood/pag...,43072&p=33004
I believe you will be a little less than your budget, and you will be able to make an edge as good as anyone. Once you get comfortable with the paper, get some of this film. You can only back up with an iron or chisel on it, or it will get so sharp, so quickly, that it will cut down into the film. http://www.leevalley.com/US/wood/pag...,43072&p=68943
I bought another one of those surface plates to keep mine on when the plates were on sale. You can probably find something that will work for nothing. 4 or 5 passes on each will put a mirror finish on something.
I have thousands of dollars worth of sharpening stuff. I have oil stones, water stones, diamond stones, and various power grinders and sharpeners. I'm telling you from 41 years of experience that the above stuff I recommended will work just fine. Paper may be more expensive over the long run if you use it every day, but I'm still on the first set of Diamond Lapping Film that is a little over a year old-I did cut some nicks in some of it before I got the hang of it.
With this stuff, you can get something dangerously sharp. Dangerous to the point that it will put you in the ER in a heartbeat, but it makes cutting wood a real pleasure. You can also flatten chisel backs, plane irons, and all but the longest of the plane bottoms.
When, and if, you do decide to spend a few hundred dollars on waterstones, they need to be flattened frequently. I flatten mine with this surface plate, and a sheet of 100 wet-or-dry. I've been using the same sheet for maybe a year-just rinse it off and let it dry between uses. Pour the slurry back on the stone to sharpen quicker.