2 prong to 3 prong outlet - with pigtailed grounds

You've got a pretty good idea on what needs to be done. Naturally, you'll be turning off the breaker to the circuit. In cases like this, I've always pigtailed the blacks together and had one connection to the outlet and do the same to the neutrals. You'll need some extra black and white wire and some wire nuts but it makes for a neater installation. If an outlet connection gets loose, it doesn't affect the whole circuit. A converted bedroom to an office wouldn't need GFCI protection but you'd add them the same way for a single outlet protection and would use the load terminals for a daisy chain protection.

Are the junction boxes metal?

Since ground wires are indeed present, you must ground the wires to the metal boxes. Use a pigtail coming up from the box's ground screw (one of the holes should be tapped for a #10-32 ground screw; they sell green ones if you want to be fancy, some even include the pigtail). Sometimes the supplied ground screw hole is accidentally used for a nail or screw. You can also add your own #10-32 hole in the box, or use a ground clip to attach a ground pigtail to the edge of the box.

Once the metal junction box is grounded, you can ground the recep either with another pigtail, or by a "self-grounding" feature on the recep which grabs ground via the mounting screws.