Best Brahms Third Symphony

My personal favorite is Brahms under Bohm, available as a 3-CD set from DG. Favorite simply because this is the reading I am listening to since my teens.
Gentle folks here pushed me towards "NPR Guide to Building a Classical CD Collection". Now is a good time to say a Big THANK YOU for the tip!!!!!!!! Its the first "guide" in my collection which resembles my fav book on the 20th century Classical, "The Rest is Noise" by Alex Ross. In short: buy it!!!! Spoiler Alert!: NPR’s top recommendations for Brahms are Bruno Walter (have it), Claudio Abbado (got it!), Istvan Kertesz (ain’t got it! ;-( )
start with those, my fav is just my uneducated guess of someone who listens to "classical" allthetime but who dropped out of Musik Skool at the age of 10 to become an "engineer"!!

Well as a Brahms freak I think you do have two of the best .
A very nice 3rd is the Charles Mackerras on Telarc CD-80450 with the Scottish Chamber Orch, His genius and the smaller force are just plain lovely .
Another fine one is Alsop with the London Phil . on Naxos, . She is a great conductor .

I'll second Schubert on the Mackerras/SCO recording, a different sound than you might be used to but very refreshing.