dont think the speedy is good as a schoolbag. i really strong suggest the BH. but if that really isn't your style even after trying it on, then go with the cabas or vavin. The lockit horizontal is fine too! or maybe a popincourt?
With your increased budget - I'd say a Saleya MM! Gorgeous Damier and it's stress-free as you don't have to worry about darkening vachetta or water stains. But if you prefer the Monogram, then it'd have to be another tote...
Honestly, the no brainer go to would be a BH or something from the Batignolles line or the LH - but you mentioned before that you don't like the batignolles line.. so not really sure what to recommend.
I'd say just go into the store and try away! You never know what you might end up loving!