Alexstraza is too slow to be useful outside of control decks most of the time, but it's definitely a good legend to keep for later
That's a pretty good mech mage deck, you can definitely get to rank 5 with that at least. Main priority for crafting should be Dr. Boom, even if he gets nerfed you'll get all of your dust back, and he fits in aggro, control, or midrange.
If you want to play control decks, Priest can be relatively cheap, there are several legendaries that are nice, but they're not needed to have a good deck, Warrior's expensive, Druid needs a fair few epics, Paladin's expensive, Face Hunter's cheap, Zoo Warlock is a pretty cheap deck, Rogue requires a lot of dust on class cards (just like priest) but is a more midrange deck that's not too expensive, Shaman can work pretty effectively as a cheap deck, and the Mech Mage that you have should be good.
So yeah: Control Priest, Face Hunter, Zoolock, Rogue, Mech Mage, Midrange Shaman are decent budget decks.