Oh duder what question; I reactivated to answer it. I've been running TTRPGS of many systems for 20 years and built a few of my own. I'll be as concise as possible. My number one DM rule for anything is, always say YES and let your PCs fail forward. If your PC wants to do x and then fails roll their roll, instead of saying No, you fail, next thing. Say, X happens but also something shit happens. Your intended action happens but it happens badly.

Exploration and Social are two different things in most games. D&D (and other D20s) and GURPS is mechanic heavy down to small scale actions but things like VTMV5 and Paranoia tend to be much less focused on mechanic minutiae. Of course, you can always pair down or combine many rolls into one roll if you want to speed up a D&D game. I think it really depends on how experienced the players, how much dice rolling they want to do, and how smooth you want the interface between in-game/out-of-game talk.

Exploration: It can be easy for a DM to make a large area, put point of interest around it and say, "ok explore" to your PCs. This can be frustrating if there is no narrative direction pointing them to locations. I've found it best to start PCs in a defined area, set the stakes and goal, then open it up t In a large, long running D20 campaigns, the most complicated I have run is Hexploration. This involves a hex map and most easily the PC to have a home base in one of the hexs, in my case the PCs were tenet farmers of a local monastery 2 hexs away. In 'downtime' they were capable of exploring a hex with a roll. The success of this roll determined what they found. If they beat the minimum, 5 they may find a small gnome village. They get 15 and they find the village, a spooky cemetery and the dungeon under that cemetery. This takes a days worth of game time to explore one hex and is subject to random encounters. This takes anywhere from 1 minute to (however long a random encounter takes) in real time. If your players are looking for specific resources, they can explore a hex and if their check is high enough, just say yes and make up an interesting reason why the resource is there. This is enjoyable for building grand shared landscapes. It can be frustrating if you don't know when to say "A day goes by; two weeks go by; etc." If you are going to smaller dungeon exploration, having one player be the active map keeper often keeps the players engaged as a team. "Where are we going, right or left?" "PCX let me look at the map." "This looks like shit where are we?" "Right here, I think we should take the right." Alternatively, I've run D&D for very fresh players and there is very little exploration. I.E. The town is lit ablaze, a cleric in shining armor guides you to a temple , magically protected from the flames. He tells you where the dragon is and points you to the path toward it. Large scale exploration can bog down a game if you don't watch the pacing. If your world building doesn't simultaneously deliver options to develop and entertain your players. I ran into a problem where I gave the PCs too many sidequests and they enjoyed the sidequests so much that I had to tone down the ongoing consequences of main quest, which would have made the game less fun (They had to finish the unfinished business of a ghost that was haunting them, preventing them from getting full sleeps. This was a mechanical nightmare in D&D and I wouldn't suggest denying your PCs full rests for extended periods.)

Social: Once again, D20 can be mechanic heavy. Roll to change their attitude, roll to charm, roll to bluff, what you say in the room as your character may or may not have mechanical impact on your roll. I frequently give them secret +2/-2 if they say something favorable/unfavorable to the NPC they are rolling against. This can be slow and I have experienced players frustrated when they lay out this beautiful soliloquy and then roll a 1. In VTMV5, what you say can give you more or less dice on a roll depending on your GM and those, during a social fight can make the difference. In VTMV5 'social fighting' pulls from another heath-like stat bar of emotional composure. I think its a good middle of the road between mechanics and roleplaying. Paranoia on the other hand; all talking in the room is in game talking and there is little distinction between the group talking among themselves in game and out of game. Interacting with NPCs is a simple rolls some Ds success/fail but the game stresses failing forward humorously and letting players burn through lives, their own and others.

Paranoia is one of my fav games to run because of the smooth rules set that has very little in the way of hard dice mechanics. I would avoid initiative for social interactions unless two PCs are trying to out maneuver each other. The more game mechanics you can roll into the actual RP, the smoother and more fun social encounters will be.

I tried to stay direct and helpful but I wrote this over a while and I've been stoned the whole time. Hope it was helpful, I feel like its not.