but I don't understand the dollar amount they show with it and how it relates to my specific situation (i.e. right now it shows medium priority 4 sat/vB is $0.58).
The fiat values of transactions fee displayed on mempool.space are for a normal segwit transaction with 1 input and 2 output which is around 140 vbytes in size.
With the fee rate of 4 sat/vbyte for such transaction, the absolute fee would be 4 × 140 = 560 sat (around $0.58 at the current rates)
Your transaction will include 1 legacy input and 1 segwit output and will be around 190 sat/vbyte.
So, if you set the fee rate to 4 sat/vbyte, the absolute fee would be around 4 × 190 = 760 sat (around $0.79 at the current rates).
For example, using your example above, if it was 4 sat/vB and I paid 760 sat as a transaction fee, how much would be deducted from 0.3 BTC?
760 sat equals to 0.0000076 BTC.