I've been asked many times what material to use for planes and I usually respond with "beech, boxwood, hard maple and white oak (maybe hornbeam as well) in that order all of which should be quarter sawn". And of course the next question is "why"?
Let's get this out of the way first, it doesn't have to be the hardest wood on the Janka scale. In fact, there are tons of species far more Janka(-y) than beech and hard maple so why not use them? The first choice is a simple one: what's available in your region and what's close enough that shipping isn't going to bankrupt you? For me that's beech and hard maple, the latter being very (very) local and the former being quite affordably shippable to my shop. Sugar maple trees are all over my street second only to oak, heck the street I live on is Oak St.
To help bolster my recommendation, I think Mr. Sellers sums up the material choice quite well here. But it boils down to this: you want a material that is dense grained, stable when it dries and perhaps most importantly, has consistent grain density throughout the material. The hardness needs to be uniform so it wears evenly so you don't get pieces of the sole with hills and valleys. Sure, you can add boxing to ease wear in the most crucial of spots but you first have to start with a solid and stable material (note I didn't say hard).
Caleb James pushes beech even more so than I do, almost to the point of saying don't bother with anything else. My issue is when you need wide pieces for large moulding planes, say chunks that need to be close to 3" wide to accommodate an iron that's 2 1/2" wide. Every lumber yard that I know of who sells quarter sawn beech doesn't carry 16/4 or even 12/4 rough quarter sawn beech. They say when it's that thickness it cracks too much during the drying process. The only way around that I know of, due to the way the grain needs to run, is to glue up a few pieces (laminate) and use that for the blanks. Now, people do say this is a no no but I'm not sure what the alternative is given how our forefathers chopped down all the big ole beech tree here in the U.S.
Ok, so why quarter sawn? First do you know what quarter sawn is? If not please start here. I think Caleb James explains it pretty darn well, and again to boil it down: it's less prone to movement long term, i.e. "stronger". Will flat sawn work? Absolutely yes but don't plan on it staying true for years to come and if you're gong to take the time to make a plane, make it right the first time.
Which brings me to the last recommendation, white oak. I'm in agreement with others that it should be the last choice, even in quarter sawn form. While it's less porous than its red brother it's still far more porous than beech or hard maple. Those open pores are just going to cause problems so I'll again concur with Mr. James here as well.
Another .02 from me to you.