The Fallkniven is convex ground, so you would have to learn the techniques for sharpening that if you want to maintain that geometry, there is lots of info on convex sharpening on this site. Its not really that hard, and I personally prefer it to a flat geometry. The other thing you could do is put a micro bevel on the edge with something like the sharpmaker (I think that may be the way there factory sharpened? FYI a micro bevel is just a very small flat bevel at a higher angle at the very edge, barely visible) and maintain that, but eventually it would thicken. Don't get discouraged by the confusing terminology, its just a complex way of explaining something quite simple
Seriously, though, there is a lot of love for the sharpmaker around here, but a few of us can still hold our own on the benchstones too.
Another vote for benchstones. Its defiantly a skill but you'll have it for the rest of your life. for less expensive stones I like Norton India stones, get a set of course med and fine, they can put a shaving edge on everything I've run into. waterstones are another option, they work great and allot quicker than other types of stones, but there messy and have to be flattened periodically. If you want a fine edge equal to the more expensive stones and dont want to spend allot of money right off the bat, scary sharp is another option.
If your going to be maintaining the convex bevel, the sharpmaker and other systems won't work (except for the edgepal I think its called), and benchstones are pretty hard to get an even convex bevel on (the bigger the bevel the harder it is on benchstones), although this is what I use. for convex bevels allot of people use sandpaper on mouse pads, then strops, etc.
