Without taking into account second layer solutions, a very rough estimate of the maximum throughput for grin is about 20 transactions/second from what I understand. Here is how I arrived to this value:
A typical transaction with one input and 2 outputs (one output to receiver and one change). This transaction will have a weight of 4+4-1=7 and because there is a limit of 10,000 weight units per block that gives around 1400 transactions per block (every minute) which corresponds to a maximum throughput of about 20 tx/s.