I currently own a 116 mistral screamer with a 5.75 sail and a 38 cm freeride fin, I weigh 75kg. The problem is I often sail where there are shallow sand bars (Minnamurra River) and I hit my fin or in the surf (Gerroa) and can't go too close to the shore. What is minimum depth fin I can ride and what type. I can buy a 20 or 25cm powerbox wave fin from overseas for about $80 but not sure if its a waste of money as it could be too small. I am only a beginner and can plane in about 15kn, but get overpowered in 20kn, I can't carve gybe yet. Was also thinking of sailing in lake illawarra but have heard you might need a weed fin but they are so expensive. I only just pick up the whole rig a month ago for $700, and didn't want to spend $200 on a fin just to get over a shallow sand bar.

You want a fin that best suits the rig/gear you have.
If this means you need to avoid sandbars to prevent ripping the fin out of the board it may be wise to.
Good news is though with a sail that size you can afford to use a smaller fin.
I usually go with the formula 5 x Sail size + 2cm
so for a 5.75m sail you'd use a 28cm + 2cm fin
If you predominantly sail where there are sandbars and weed, consider using a weedfin.
Go smaller again for waves. Maybe around 25cm.

Go with a weed fin or invest in a multi fin board, some twinzers work pretty well with that kind of sailing.
Kind of a pricy solution though for where you choose to sail.
The most economic solution is to find a better place to sail. Sailing in shallow water can be risky, I guess you haven't been launched yet, but you will eventually, landing in deep water doesn't hurt like getting smashed on the bottom. An old girlfriend of mine broke her arm getting launched in about 50cm of water.

Get ya self a 30.swept back style or dolphin fin as some people call it .
it will shy off objects rather than grab ,like a pointer fin .
most shops have a good selection of second hand fins ,give them a call .
Im sure you will get one for $80 that will do the job .I always
head for the second hand fin box when I see a shop .you can never have too many fins .

and welcome to the magic world of windsurfing

I sail in similar , shallow water and or rocky areas. 70kg. My formula for you is 30cm, depending on the fin area maybe 28cm. The size your using is large, while your sail is small.

You can gain, some bottom clearance with a weed Fin.

The suggestion to change to a multi fin board is great, if you can afford it, using a tri fin setup , with the weed Fin as center would be a hot ticket.

For that set up an 18 cm delta fin will solve all your problems and would probably allow for more sail should you need it.
Pro,s : Cheaper than buying a multi fin board.
Even if you do hit something it won't damage the board/ or you.
Available in P.B
Opens up sailing in places that were previously not an option.
Advertise it on sea breeze at the right price and it will be gone the same day.

Con,s : Relatively expensive
Not as loose as a weed wave type fin.
Can be a handful in choppy conditions without the right technique.