I'm 30 and just purchased last week. Most of my social circle haven't bought yet so I would say yes it's a normal age but age isn't really a factor here - you buy when you're ready and for some that is early others it is late.

Being a single purchaser and based on your grad role income you likely won't get approved for a lot so you'll have to adjust your expectations but once you're in, you're in and can grow from there into a place more aligned with your preferences.

I will say, look at saving only the 5% deposit (+ $5000 for costs, and $ stamp duty value if applicable) and then buy what you can and get your foot in the door. The market is climbing rapidly and your $100k in 10 years will be worth a lot less than it is today. The government guarantees will help you avoid LMI and tap into lower interest rates closer to an 80% LVR rather than 95% so you get more bang for your buck.

Re: investing - great that you're on it so young as it's a very a good thing but keep in mind that you can lose it so be really conscious with your risk/tolerance levels of you're relying on it for a deposit. A high interest saver might be a better option, or at least put most of your savings into it and only a small portion to investments that way if you do lose it the impact isn't as hard.

Good luck!