That guide is quite good on how to get from end-of-story to the real endgame. But for early game (leveling from 0) I’d say this:
Demo Woman is in my view the best tree to start with - Iron Bear is excellent in non-Mayhem and this tree offers good IB buffs. Deadlines, Grizzled, and Stainless Steel Bear are excellent for IB (but Grizzled is much better with more points. Max it out, as opposed to sticking 2 points in it and then leaving it alone). Means of Destruction and Torgue Cross Promotion are good in general but will obviously perform better if you have guns that do splash, so look for Torgue and Maliwan guns in particular and Heavies as emergency 2nd-wind weapons.
Pull the Holy Pin may work if you like killing things with grenades, but I think of it as a utility skill that does more for you in endgame (it is also very good with Tediore chucking). Auto Bear is well worth it for 1 point.
Vampyr is excellent at keeping you alive. You may not even need 5/5 if you use grenades that have divider/mirv/bouncy or some combination thereof.
Avoid Explosive Punctuation. It’s much less effective than Grizzled. Avoid Why Can’t I Carry.
To the Last is well worth 1 point.
Short Fuse is really really good. Once you are level 28 you’ll have this and I would start building another tree.
Shield of Retribution has a combination of good offensive and defensive skills; Bottomless Mags will let you fire almost endlessly and provides additional utility, especially with Iron Bear. Because IB will still be good until you’re advancing through Mayhem, I’d therefore go for Bottomless Mags.
For general play take Cloud of Lead; Matched Set is only worth it if you find yourself using mostly one Manufacturer’s weapons. Dakka is only useful in co-op, but if you are playing co-op it can be a good buff for IB.
Then take Redistribution and Scrappy. Stoke the Embers is fine, but to make good use of it you’ll need to go out of your way to ensure that you’re using incendiary as much as possible.
RPMs is excellent. Max it out. To my knowledge Rushin Offensive is buggy at the moment so you may want to avoid it; its healing may also be redundant with Vampyr if you’re chucking grenades regularly.
By the time you max out RPMs you’ll be level 43 and will probably be done with the story; at that point you’ll want to start thinking about moving to low Mayhem levels, which may mean rethinking your build.
As mentioned, Moze will do well with guns that do splash damage. For your COMs, look for ones with skills you use and which will enhance your playstyle. If you’re lucky enough to get a legendary COM to world-drop early, you may consider a re-spec to make better use of it, they can be game-changers early (Mindsweeper in particular is really powerful). For shield, I’d look for something that has good recharge statistics even if the capacity is meh. The adaptive affix on shields is also one that I like.
For grenades, Trackers with combinations of Mirv/Divider/Bouncy affixes interact well with Means and with Vampyr. Look out for these in vending machines.
Consider saving Eridium to buy shields and grenade mods with action skill end bonus elemental damage anoints from Earl’s machine. These anoints are game-changers and may even be worth save-quit farming the vendor to get good ones.
Once you are able to equip artifacts, Snowdrifts have good movement utility and Ice Breakers (non-legendaries) buff your damage if you do a lot of cryo. Others can be tough to make good use of bug you may not have much choice at first. A Victory Rush (legendary) provides excellent damage and movement speed for leveling through the 30s/early 40s. It can be farmed from Thunk and Sloth in Konrad’s Hold once you get that far.