Any weapon is workable if you take the damage perk for it. Single shot Rifles and Shotguns are clearly the best, due to the synergy with stealth and relative easy availability. Maybe heavy weapons would be off the market, since they are fairly scarce (at least early) and ammo is often tough to obtain. Mele is actually a lot of fun, it just requires you to either abuse power armor or stealth to get in range alive (at least on survival). With how plentiful they are, I would say you could probably rely on explosives as a main weapon if you wanted. Pistol is definitely the most viable weapon type after rifles, though. The perk is easy to get, the guns and ammo are plentiful, and you can max out the mods without max gun nut perk. My next play though I am going to try an explosives/mele/pistol build, because my wife has been doing that and it looks like a lot of fun. Only bummer is I miss being able to use VATS to toss grenades....
Powered armor, meh. Seven suits in my home base and a safe full of fusion cores, and I generally only use it for a story fight (taking the castle) where I feel I will need it or to finish clearing/haul loot when I find a suit. I have not been looking for it or advancing the main quest and I already have a modded up 50 suit and a X-01 with a couple pieces missing that I randomly came across. Not sure if I am interested enough in armorer this play through to do the jump jet tactic or not, but Tesla chest frying the trash adds in certain fights has been fun.
Also, Vorph is 100% correct about the sniper perk being a complete waste. Two stabilize arm mods (easy to unlock, especially on leather armor) pretty much negates all the weapon sway.
As for Asbestos vs anti explosive, I happen to like being able to take hits from energy weapons and having a lot of energy defense will make tackling Forged and Institute Synths a lot easier, but for just about anyone else the anti explosion mod is likely superior. I personally just dart to a new spot and re-stealth, so its not as critical for me (actually been slotting Rad Defense for the fucking cultists) but if you are engaging Supermutants and Raiders a lot at lower levels, especially without abusing stealth, you kind of have to have it to offset the infinite grenade cheese. I will say that while it does not help for the grenades themselves, having Toughness and stacking over 100 DR makes you able to handle incidental fire a lot better, but I understand why he thinks that perk is a waste. I happen to like it, since it makes me less dependent on a DR based main clothing slot and makes me very tanky, but if you are a full on reloading stealth cheeser, its probably not essential. If you fuck up and play through the mistake a lot like I do, its golden, though.