Originally Posted by BicycleBicycle

If you buy a new fixed gear for not much more than the wheelset, you're going to get something with a similar wheelset and similar parts.
Your frame will be better (sometimes much much better) but not much else. You'll probably have some nice alloy bars too, but they won't be like that great.
Most sub $600 completes, for whatever reason, come with absolute crap wheels.
(That only changes when you go to like the $800+ range).

If you buy wheels, you'll notice an immediate and DRAMATIC improvement. IMO nothing else has made me smile more, and nothing else has made more of a noticeable difference.
Just from personal experience, I've noticed that wheels are the best thing you can upgrade and make the most difference other than your frame in terms of how your bike rides.
Each part will make a difference in a mutually exclusive way. Eg. If you replace rims, you'll notice. Hubs, you'll notice. Spokes, you'll probably notice. Hell, even the cog sometimes.
Your rims are probably boat anchors, and you'll probably notice a very dramatic difference as soon as you get new wheels.

If the rest of your bike is sized in industry standard (which it seems like it is) eg. 1 1/8" headset, 27.2 seatpost, ISO or JIS english threaded BB, etc. Then you can just upgrade as you go.
I would check velomine for wheels personally. I've seen some pretty good wheelsets go for about $120, and very good ones for just a little over $200.
I wouldn't settle for anything less than sealed cartridge formulas for hubs, and anything less than H+ sons, Mavic, et al. for rims in the $200 range, and you can get some classics like the CR-18 (rode these for a while and loved them 22.5 mm inner width) for the $120 range. You'll also get DT Swiss spokes on most of their builds.
This is all velomine specific. In almost any other place (even online), regular unsealed deep aftermarket wheels go for $100-$135 each!
There's also the difference between the stuff that comes stock on most bikes, and the unsealed that you can buy aftermarket. With stock being pot metal flared cups waiting to happen, and aftermarket being some decent stuff (but I personally still prefer cartridge bearings).
Sealed cartridge isn't the be all end all, but it's typically a good indicator of quality. Many aftermarket brands make great unsealed wheels that you'll just have to maintain, but IMO buying new unsealed wheels is only worth it if you're doing a conversion and you want a basic wheelset just to see if you like fixed gear riding.

Eventually you can replace the frame.

BUT, keep in mind that you have 650b wheels. If you're happy with that wheel size then go for it but keep in mind that most fixed gear frames are 700c.
I would check to see if 700c's would fit that frame (Looks like they would to me). You probalby won't be happy when you find that many frames are just not built for smaller wheels.

Anyways, point is, I wouldn't buy an entirely new bike unless you're willing to spend something close to $1000, becuase most of the parts on the mid range builds will be exactly what you have now.
Also, I would look into getting 700c wheels, or look at some of your dream frames and see if they fit or are made for 650b's. I would imagine that most frames built to ride with 650b's are like fgfs frames or some kind of "do it all" frame that won't really be all that great in terms of agility.

If you look around, and find that 700c won't fit, and you don't want to spend a ton of money, there's always the kilott.