I am biased because I just cannot figure out Monk, so I'd go for champion. You got the katana you can pump upgrades in for decent damage, then keep the whip as secondary plus the talent that equalizes upgrades with your secondary weapon.
Then you got the nice weapon ability of the whip but the katana for main damage and also some extra mobility.
Monk is all about energy ability spam, it works well with anything that wants constant wand or artifact charging thanks to meditate. With the subclass talents maxed out and clever use of something like staff stance into meditation your recharging has close to 100% availability and costs half of what it usually would. The usual thing to do with them is go full into unencumbered and wands then spam meditation for wand recharge and healing between. You use dash and dagger weapon abilities so that nothing gets in melee range. Dragon kick is a solid "oh shit" button if something does.
You could go either way but with a RoH and a corrosion wand you'll be one kitey boi as an unencumbered monk.
My usual rule of thumb for the choice is "did I find mobility tools (RoH, chains, hourglass) and a good offensive wand?" If so I usually go wand monk.
On the other hand if I found an early t5 weapon or a viable +2 t4 I go champion and immediately dump upgrades on it to ~+6. If you do this grab the shared upgrades talent, it will let you use your t5 as an upgrade holder and will boost any weapon you equip in the second slot to the same upgrade level. Any t5 works here, you don't actually have to use it unless you want to or it has a good weapon ability, just leave your upgrade stick equipped so that the weapon you are actually using receives upgrades too. If your upgrade stick is a greatshield or something you can always transmute it the next time you find a transmute scroll. Crossbows are especially good as offhand champion weapons so be sure to buy darts at every shop in case you come across one later - 5x5 tile AOE dart effects are amazing. If I find a crossbow before I make my class choice I usually choose champion.
Wand monk is the mobility king - you'll want to abuse meditate to recharge your wands and any artifacts, use Swift Equip to equip a staff for the staff stance for massive evasion when needed or a dagger to teleport out of danger then go back to your t1 gloves for extra energy when you zap things to death. Split enemies up, don't tank, use dagger blinks, monk dash and staff stance to avoid taking damage. Think of a dagger as a reusable six tile blink stone and just wand everything to death. If all else fails and something's in your face dragon kick it and run away. Go all in on the subclass talents if you're going to play wand monk.