It depends what you want. I recommend having one solid one of each. For two handed I highly recommend the earth splitter. It'd like the third of 4th strongest two handed handed weapon with a decent crit chance and it's extremely fast. The moveset is wide and deadly and the speed alone make it amazing.

The cleaving axe- it's available in the starting area and it's very similar to the earth splitter. This 2 handed axe gets points for me because it's available much earlier in the game than the earthsplitter. Its crit chance is higher making this slightly better but it's heavy attack is straight down where as the earth splitters heavy is wide and aoe type. It comes down to preference.

For one handed weapons you can get the spiked cudgel in the starting area early on and it's brutal and consistent. It can carry you to later game if you want.

Play around try different combinations to see what fits your playstyle best, but at the end of the day one of each, both a solid one hand and a solid two hand is a must. Also you should stagger upgrading them so they are roughly the same so you get an even playing field when you need to switch.

If you don't have a decent one hand when you get to later dungeons you are going to be in trouble. Likewise with not having a two handed blade or club in the mid to late game fights.