@Fishbreath
Caster duels are like that. The one with the biggest range or most CC usualy wins. You can do something he can't though, which is outlast him in lane. As Ryze gets more money and levels, he becomes increasingly harder for enemy casters to fight, because he can gain both damage and survivability from items like banshee's veil, that one item which will mess up most caster's combos, including Brand. You can't, however, beat Brand early on, at least not reliably. His range is superior and he can use his E Q W (+R) combo on you before you get him in range.
You should try to outfarm him in lane so you can get your stuff faster. Try to get a teamate to gank him, preferably someone with a stun so you can unleash your full combo on him. You could try to out-harass him since your cooldowns are shorter, but you lack some power early on compared to him, so that might just not work.
Ryze's early game is a bit meh, but he becomes good considerably faster then most casters, plus he's pretty tanky since you get alot of power and survivability from frozen heart, rod of ages and banshee's veil.
Pretty general tips. Don't play casters that much, even though I have played both more then once.
Also, one more general tip: if you're having trouble surviving in the early game, consider getting a catalyst as your first non-boot item instead of a tear of the goddess. If you play somewhat safe, that item lets you basicaly sit in lane and never have to go back, even if you get harassed some times, so you can focus on getting CS.