Grammar – ‘Me Doing Something’ or ‘My Doing Something’?

A's marked infinitive to continue is becoming acceptable in informal registers, on the analogy of told her to continue, but is generally deprecated in formal registers.

B's inflected finite form continues is accepted in BrE, at least in journalistic contexts, but the complementizer that is rarely omitted with this.

C's finite past form, continued, is not employed: recommended can only take a subsequent action as its complement.

D, with the 'mandative subjunctive' (uninflected base form of the verb) continue, is preferred in AmE and is returning to use in BrE.

Both are grammatucal. But the use of the first preposition of is old-fashioned in modern English. So the second sentence as follows is far more common and idiomatic:

The planet is the size of (the same size as) the earth.