Don't be so quick to dismiss Dad.
The appearance is of course subjective...but, a lifted truck IS more likely to roll.
Not ALOT more for a 3" lift, but more.
The higher your center of gravity...the slower you have to go around corners, etc....its just physics....not your dad's mistake.
If you are a new driver (16)...learning to pick your line is more important than getting tall.
The taller you are, the more likely you are to get into trouble if you haven't learned how to pick lines.
Lines are the way through the terrain that keep your tires on the ground where they can push you/hold you up, and not get truck parts cought on obstructions, or get you perpendicular to the slope, etc.
If you make a mistake, you can roll over/fall off a cliff, etc. (Bad things)
If you make your mistakes while short...you are more likley to be able to recover/survive...kind of like learning to tight rope walk a few feet up before hitting the big top circuit....
Your dad will be watchinng you like a hawk....if you bang up the truck...it won't instill confidence....get good at it first...THEN upgrade components as needed.
Add armor (Plates, sliders...) before height - you will NEVER be tall enough to clear everything...you will need to slide over the larger obstacles anyway.
Reinforce weak links, like steering, etc...
in short...make the truck as bullet proof as you can so you come home unscathed, and instill some confidence that you are a mature, careful, driver.
When you get to the point where a lift is a potential reality...do it in stages...get parts that work for 1.5" as well as for 3", so nothing is wasted, and you (And your dad...) get used to it before going up again.
A t-bar crank and shackles is about $50, and is HALF (1.5") of the 3" lift.
The fatter tires help more than the taller tires...and you can do up to about 12.5" section width to 11.5" of section width depending upon your turning radius needs.
If you can trim the plastic around where the mud flaps mount a bit (an inch or so...)...you can get much larger tires under there.
Good Luck!