The 7000 is a great deal.... If you have optics to mount on it. Like most heavy barrels it has no iron sights so you have to factor in a scope or you won't be hitting much.
The upside of the 7000 is you get a target barrel, a stock with sling attachment studs, nickel plated mags, last shot bolt hold, and scope rings.
None of these are offered on the base 10/22 synthetic.
The major upside of the 10/22 is its rotary mag which fits nicely inside the stock, the upgradablility and availablility of aftermarket parts, and the huge amount of helpful information out there.
The 597 is probably the most debated rifle of the three.
Those who like it, like it a lot. All others seem to hate it.
I won't touch this one .
When I was in your shoes a while back I ended up with the 10/22. I am now looking at giving my dad a new .22 for Christmas and I am most likely going to give him the 7000. Having handled both I think it's more of a personal preference than anything. If you can, go to the store and get a feel for the guns. Ask a lot of questions there. Find out about their warranty and whether or not they can fix it in house or if they send it back to the manufacturer. Find out if they offer any package deals. You may end up finding something you really like.