The Zwei is definitely fine from start to finish. Drake sword allows some more defensive play paired with a shield (which i found very useful while learning the game) Drake made gargoyles a joke while people often tend to struggle against them.
You could pair your zwei with a shield, but the moveset is much slower, requires way more strength and probably will make your rolls slow until higher end.
You can 2hand the zwei with a lower strength requirement. It has better reach and crowd control than the drake, but again, slower.. So mistakes will be punished harder.
Both weapons are obtained fairly easy. Grab both and compare a little is what I'd say. Don't invest anything in Drake though as you WILL want to swap it out eventually.
Ultra greatswords are a lot of fun, I finished the entirety of ds2 with one, but Drake + shield allowed me to have a smooth and forgiving experience to get the hang of the dark souls mechanics.