Hi Brandeeno and welcome to this forum!
Sad to hear your first batch failed, I've made several cheeses with store bought pasteurized milk and no CaCl2, if you didn't get a firm curd set maybe you didn't dilute your rennet and mix it in enough or maybe it was no good? CaCl2 in my experience just helps in getting a good set.
Good questions, aging at room 70-80F temperature is in my experience a non-starter as too easy to easy to get infected with air born spores etc. So I would go for fridge, even at 35F it will age, just slower, so if you could raise temp a little to 40F that would help. But, key especially in fridge is maintaining a high humidity.
Have fun, more details on your first batch would help identify the problem, (ie milk type, rennet source, how diluted, temp of milk etc).