If the rocks are loose and resting on top of the soil, then renting a skidsteer w/ a rockhound would be appropriate. If rocks are imbedded in soil and bound w/ vegetation, then a york style rake might loosen them for collection. The large rocks may require collection by hand. I recently saw a member post that discussed a company named ridgerunner. Or roadrunner, see photo.
They make several products. One is a reverse mounted york style rake that mounts SSQA style on the tractor FEL. Keeps the rock collection out in front of your field of view. There may be other collection methods, as folks offer suggestions.
The photo identifies the company, NOT the specific implement they make that would collect rocks. J Bar mfg in trion GA offers $ landscape rakes, direct sales. Skidsteer /rockhound rental is expensive and requires some practice for efficiency. Myself, I'd locate a landscape contractor who owns this equipment and seek an estimate.
A tine tiller is a bad idea, if rock collection is goal, if you rent, the excessive rocks can dent the housing and rental yard will have a damage issue. Tillers are self destructive, excessive rocks can bind and break chain drive or gears dependent upon hp. Reverse tines are said to bury rocks, no experience w/ them. Forward tines will generally bring them to surface, then a rockhound would clean them up. Still advise, get professional estimate for the project, save some heartache or not. Farmers use rock pickers, big and bulky for small applications, rocks must be loose, and on the surface. Farmers aren't picky about 2" size. They roll them in the spring if at all. There are rock picking tine buckets for the FEL, ok for farm fields, not landscaped lawns.
Would not worry about sub-surface rocks, roll the lawn in the spring, just not this spring as still snowing accross the country. Just collect those that are visible. You will never live long enough to collect all the rocks in the 12 " of earth just below your feet.