Praxis v T1 Amarr Battleship.
In virtually all cases the Amarr T1 battleship will out perform the Praxis. For example, An Apocalypse, a good mission battleship carries eight turrets to the Praxis’ six - OK, the Praxis gets drone and missile benefits and a couple of missile slots, but that’s a couple more weapon systems to train. Assuming you’ve got the PG for six turrets and two launchers.
The Apocalypse’s bonuses to range and tracking equate to more damage at the same range and better application.
Once you get to Amarr Battleship IV, then the damage bonus on an Abaddon is 30% compared to 25% on the Praxis. At the same point the Armageddon has a 40% drone bonus compared to 25% on the Praxis.
If fitting for Armour, the Amarr Battleships uniformly out perform a Praxis. With an Amarrian ship you are going to be armour fitted, and use Energy turrets - but that’s Amarr for you: use a brick to bring the Light of God to the heathens.
As others have said, you don’t need a Battleship for Level 3 missions, a well fitted battlecruiser works nicely (I use a Harbinger). Don’t aim for a Command ship for mission running - they are a long train and not needed. They have their role and are expensive.
The Navy Harbinger is a good upgrade if you’ve the ISK.
It is seriously worth training the basic skills - “the Magic 14” as they are known (Google it). They help with everything you fly, then add in the relevent weapon skills and defensive skills and it’ll make a good base to build on.
The Praxis us a ship with a low skill threshold, yes, but once you’ve modest skills then it’ll become a limiting problem for you.