I have ran a game for awhile now that my players loved to play and it was great to DM but what I think is surprising in some ways is that I did by basically cutting everything.
The game used the basic six stats from dnd str, int, wis, dex, con, cha.
but in some ways that was it. I didnt let the players choose classes or races they were all just human people, their equipment was chosen based off of what matched their stats and they were kept rather poor. Such as someone with high int might be dressed as a scholar and maybe have a scroll and/or some writing material. Someone with high str might make sure too keep a good pair of boots and maybe own a weapon.
Anyone could use weapons without penalty and anyone with a good int could cast from scrolls. (at the time I didn't have them vanish either) Despite being poor it wasn't hard for the characters to quip themselves with quickly made clubs and sharpened sticks as spears.
I told all the players they could pay for further training and maybe gain some kind of proficiency (or even 3rd edition dtyled feat) but that the amount of training they could have would be limited by level.
And that was basically it each player could quickly roll new characters if one died and those with a good wis score might receive divine help. The players were ran through some old TSR adventures and they had a great time.
There was no need for skills (which I think hinder role play) or even to hit charts or saving throws. It wasn't hard to balance the adventures either and once PC's got some feats it equaled everything out pretty well when compared to the to hit bonus and such that they weren't getting.
I still think my favorite part was how quick and easy it was to roll up a new character but It still felt to everyone like they were playing dnd. And if a character died then we didn't even need to pause while a new one was rolled up.