A chicken tractor (of any sort) will not "help keep your lawn in good shape". If you move it frequently enough (potentially once or twice a day) and your grass grows well enough all year round, you can keep the impact of the tractor from being *hugely* noticeable, but no matter what, you WILL have visible chewed-and-stomped-and-scratched-down rectangles where the tractor has recently been, and you WILL have poo lying around in those places, and it does not disappear as rapidly as you might think, especially in the spring before flies have really gotten going. Also note that in many climates there are times of year when the "chickened" areas won't grow back for *months*, and/or times of year when you may not be able to move the tractor at all. (And small tractor-style coops *suck* for overwintering if you happen to live in the North)
If a Better Homes and Garden style lawn is important to you, I would still of course encourage you to get chickens
but instead build them a PERMANENT, fixed-location coop with run. You can make it as purty (or not) and landscaped (or not) as you wish, but it will prevent the chicken issues from spreading themselves thinly all across your backyard.
If you want the chickens to be able to graze your lawn, which is certainly laudable, you might consider either supervised free-ranging if you have a well-fenced yard and some free time some afternoons, or making a 'day tractor' type pen so that you can move them around in a easy-to-build lightweight pen as lawn and whim permit, but they stay in the coop/run the rest of the time.
For whatever it's worth (possibly not much, as everyone's climate and soil and lawn are different!), when I had my 4x7'-footprint 3-chicken tractor (it had the house part up above the pen part, so total square footage was a bit bigger), I used an area of lawn that was probably 80x40', moving the tractor every day, and generally had about ten days worth of conspicuous "tractor trail" behind it, where the grass was obviously-thrashed and pooey, and some shavings from the house portion of hte tractor had spilled out. I could have moved it less than daily but then the tractored area would have been REALLY obvious and taken longer to grow back. This is on naturally-well-watered (low spot, clay) mild-summer fescue lawn which probably grows about as fast as anybody's in midsummer and faster than a lot of 'em.
Not *necessarily* trying to talk you out of tractoring chickens, just want to make sure you are realistic about how it is likely to go
A fixed-location coop for (say) 3 chickens does not need to be a huge commitment of area, you'd want at least 4x8' of run space preferably more, and somewhere between a 3x4' coop and "however big you care to build". (Bigger indoor area is better in northern winters).
Go for it, chickens are FUN
Good luck, have fun,
Pat