As with all PMD games, you can only evolve after you've defeated the main story line.
After the player returns to Pokémon Paradise and completes one dungeon, both Pokémon and recruited Pokémon may now evolve if the player chooses to evolve them inside of dungeons. The leading Pokémon may also be changed as well.
I would go for Axew/ Oshawott. Dragon Rage is really useful, since you will face overpowered enemies like Bravairy, which will barely take any damage from you; D-Rage will do 30 HP damage each time (not 40 since this is PMD). Oshawott will provide typing coverage, since Axew is weak to Ice; Tepig will work in place of Oshawott.
Considering three other Pokemon join your team later (idk if you mind spoilers so I'll leave it at that), the Dragon/ Water type combo gives the widest coverage in light of your future team.
Pretty sure there will be Ice TMs around as well, so Oshawott will be able to learn an Ice move to for more coverage.