Securing 2-Post Rack to Floor

You should use bolts. Put a 2x backer board under the subfloor too, attached to the floor joists if possible. Those racks can put a hell of a lot of torque on the anchors. You may want to anchor the top to something too. The two post racks can be wobbly, especially if loaded with heavy equipment.

Well, that rack constitutes quite a long lever acting against those relatively short mounting plates. I would have to do an engineering analysis the likes of which I don't have time for to give you a good answer as to what would be best.

There is no question that using bolts through the subfloor with appropriate washers can give you a stronger and safer installation than lag screws. Lag screws are limited by the holding strength of the threads in the wood. Through bolts are limited primarily by the strength of the bolt. Don't count on the finish floor for anything. It isn't structurally secured to the subfloor. You may need to add a doubler beneath the subfloor to get it stiff enough to keep the rack from rocking more than you like.

IIWY I would use grade 5 bolts that fit the holes in the base, big fender washers and a doubler.

IMHO the top should be secured. But the product seems to be designed to allow use without doing so.

Grade 8 should be OK in this case. Grade 8 is stronger, but not always a better choice. Grade 5 bolts will give some warning when they reach their limits because they will stretch a bit. Grade 8 bolts are harder and often just break when they reach their limits. In your case, either will probably start to crush your subfloor well before reaching their limits.