Having reached the point where I am happy with solving with basic methods such as LBL an 8355, what would be a good introduction method to intermediate solving?
There are basically three methods nowadays that people use:
Roux
ZZ
CFOP
With all of them you can get really fast, it comes down to personal preference. Roux for example is very heavy on M-turns, so if you don't like those, roux might be not the method for you.
I really encourage you to look into all methods and then decide which one fits you the best.
And i think you should try the methods in the same order as listed above, as for example doing cfop and then switching to roux is a very tough thing.
Part of an introduction to CFOP could be using a 4LLL (4-look last layer)
That is to say, completing the U layer last and in 4 steps.
This can break down as a 2-step orientation and a 2 step permutation.
here's the simplest efficient way I know to do that: http://solvexio.cf/app/#/FIXLL_OnePage
Also if you think a corners first method would be interesting, then check out LMCF.
It can start with little memorization then expand greatly for as much as you want to learn.