Looking at bowhunting this fall, and a buddy of mine suggested the infinite edge a when I was looking into it a couple years ago, but another buddy has a Samick Sage set up with the same sort of peep sights/stabilizer/rest that I normally associate with compounds.
Is there anything that really justifies the compound's $150-200 price increase over the recurve?
The only archery experience I have is with single wood long bows in the 50-60# range.
Both of those that I have eventually broke (probably due to not oiling enough).
Looking for some with more range/practical accuracy to hunt with.

The faster shot, less holding weight, less shot vibration, MUCH shorter overall length, and ease of proficiency justify what is a more expensive bow to manufacture (and therefore more expensive to buy).

Olympic archers use sights and stabilizers, but rely on a proper and consistent anchor point instead of a rear peep.  They're also shooting at a small 10 ring from extended distances, and require a little more precision than what instinctive shooting offers.

I'm all for using what you want, but by the time you dress up a recurve to mimic a compound, the allure of shooting traditional for the sake of shooting traditional seems lost to me.

+110%! Zero desire to dress up my recurves. 

2 different archery experiences - pick what interests you and press on.

You are going to get more practical hunting range with a compound; if you go traditional you do it for the enjoyment of the experience. I could have killed 7 deer easily the last 3 seasons if I still used a wheel bow that I passed with a recurve. If maximizing your chances of putting deer on the ground is your goal then get a compound.

Traditionals are great for traditional shooting. Dressing a traditional with all that and you may as well get the compound. I like my traditional bows, but they do not come close to compound in every category. That being said, the Infinite Edge is a great bow for the money.

A compound bow is considerably easier to wait for a moving target ,such as a deer, while at full draw to stop for a shot.  
I agree w/ the other's posts as well as far as dressing up a recurve bow.  
The mechanical advantage of longer range and more draw weight combined w/ the ability to hold it at full draw and get a better shot vs a recurve while hunting is a big deal.

I'd say stay traditional if you go traditional. I just got the itch myself but I also just picked up a new Hoyt Pro Defiant. Pushing 300+ fps with a 66# draw weight. 

I started shooting a compound back when 45% to 50% let off was the norm and just before eccentric cams started showing up when arrow speeds were about the same as recurves - in the 175-185 fps range.

Now with let offs in the 75% to 90% range, and arrow speeds in the 250-300 fps range, I put them in the same category as in-line muzzle loaders.

I much prefer to hunt with a traditional muzzle loader (.54 Hawken or a .58 rifled musket) because the modern in-line black powder rifles lack the feel, the history, and quite frankly the intent of hunting with a primitive rifle.  They suck all the fun out of it, and make it a lot less rewarding.

In the same way, modern compound bow takes much of the challenge and fun out of bow hunting.

I do make a nod to technology in the form of a plain pin sight - but no peep, no stabilizer, no fancy rest, etc.   It's about the right balance between traditional and practical, and makes the skill of the archer in both tuning the bow and making the shot much more important.

For fun's sake, is there any advantage to buying a compound bow and then switching to a traditional bow.  Talking only target shooting, not interested in hunting.  What I'm asking, does the compound offer and learning to aim before transitioning to a traditional bow?  Or just skip the compound and go straight to learning the traditional bow?

Compound bows are easier to shoot, hold, and requires less practice.  Recurve you need to practice a lot. Harder to hold on a game animal for an extended period.

Recurve bows are traditional until you throw all the accessories on it. If you're getting it just for some fun target practice get a bare bones recurve and learn to shoot instinctual. It is a different shooting style than a compound though, so if you switch over to a compound later you have to relearn a little bit but the compound is way easier.

One of the challenges of a recurve is learning to tune it properly - adjusting string length and thus brace height, adjusting the rest or shelf to deal with paradox and selecting the right arrow spine and getting the nocking point in just the right location.

None of it is all that hard but it take a little more work.  But once you get there, you've got a light weight bow that is quiet and a pleasure to shoot.

Arrow flight will be a bit slower and the effective range will be commensurately shorter, and you won't be able to hold the bow at full draw for a significant period of time, like you can with a high let off compound, but it's much more satisfying over all.

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My advice though is to get both if you are not sure.  

A Samick Sage is a great recurve and the cost is only around $130.  I recommend you start out light with 30# or 35# limbs and then step it up to 40# or 45# limbs once you've developed good technique.  Starting out at 40# or 45# makes the learning curve too steep.    As a take down it's slightly heavier than a one piece wood bow, but it's also a take down and is very portable as well as easy to store.