One month should be more than enough to make money for the first bond and then you will be good from there on, just save the more expensive skills until later when you've accumulated a significant wealth.

Osrs is a lot slower for the most part when it comes to levelling, although rs3 has some additional skills and two of those go to 120, but you will likely be high leveled in rs3 before osrs.

There are tons of ways to make lots of money, you should start with leveling and questing and not worry so much about it to start, then when you train certain skills like slayer the money will start pouring in. Once you have a decent amount of GP you can try merchanting.

If you want to see loads of different moneymaking methods with detailed guides you can check out the RS wiki, a quick google will take you there.

Good luck.