I used to handle biscuits as little as possible, but I started giving them about 5-7 kneads before rolling them out, not being rough mind you, but enough to get the gluten activated so that the dough has a bit of strength to rise "up" instead of spreading. Another way is to place them on the pan so that they are touching, they will be less likely to spread and will rise higher.
You can also try a recipe for cream biscuits. The cream replaces the shortening/butter and the milk, and is super easy and tasty!
Cream Biscuits Recipe - Food.com - 263699
If you have self rising flour, you can use just that and the cream omitting the baking powder and salt from the recipe (the self rising flour has these added already.
Cream Biscuits Recipe : Paula Deen : Recipes : Food Network
Cream biscuits might be my favorite method.
Don't expect fast food style biscuits from a home made recipe, I don't know what all is in those biscuits, but it's not easy to duplicate that type of result at home, I'm sure that there are additives in the mix that is used.