I used every mode of transportation (except driving a car myself) during my trip and managed fine. About the beach, that was my primary purpose in going to Tulum (I figured I would do a quick walk-through of the ruins since I was there). I strongly encourage you to go beyond the beach right at the ruins. You can walk to the north part of Tulum beaches or take a cab there or to the south Tulum beaches. I walked to El Parasaio beach club, and that was a great beach. I heard the beaches further south were nice too, but unfortunately, I didn't get to them.
Here are some instructions I copied from a post before my trip about accessing the beach from the ruins:
"...you can take a cab on the short 5 minute ride to the Tulum beaches OR when standing outside the Tulum temple wall waiting for the tram pick up, look to your left and notice a long road heading into the jungle. If you walk down that road, in 3/4 mile you'll reach El Paraiso (cut out to the beach as soon as you find a way, or at Zacil Kin, whichever comes first)".
Getting around PDC is really easy because the streets are a logical grid system. The only thing that confused me a little bit once was that Jaurez is the divider between north and south, so the numbered streets repeat (kind of like in in Washington, DC but not nearly as confusing because it is just north and south)!