First of all, I dont know who told you that Modified Bitumen is the best type of roof. The best type of roof is subjective, and is answered by "It Depends"
Since you are in a row home in DC, (I am in MD) you do not want to use either EPDM or TPO. These are true single ply roofs, and are not tough enough for the environment they would be in, so a multiply Built up roof, or a two ply SBS hot mopped modified bitumen roof would serve you best. I would not use a torch applied Modified Bitumen roof, as the risk of fire is very great with these.
With either your flashing is very critical, Im thinking you have a short parapet three sides and a gutter rear. Is this correct?
Tear all of the existing roofs and flashings off down to the deck.(I assume wood)
Inspect the deck for damage, and replace any bad wood. (If your deck is 1 inch full thickness roofing planks, you might need to re cover with plywood.
If you decide on a 3 or four ply BUR with type 4 fiberglass felt (I would) dry nail a G2 (4601 Type 2) Glass base sheet down with cap nails. Nail 6 inches OC in laps and 16 inches OC Staggered down the center one third in from each edge.
Install cant strips at all rising walls.
Mop three or four plies of type 4 felt lapping correctly 34 inches / Number of plies. (Roll width - 2 inches for headlap/ plies 3 ply lap is 11.33, 4 ply is 8.5 inches.
Modified Bitumen is OK, the problem is that any schmuck can buy it, and ruin your roof. You need a kettle for hot with BUR, and most schmucks dont have one.
You can also go cold process. I would go BUR with an aluminum surfacing.