To

I haven’t being in Capri, but I’m going in a few weeks so this is based on what I’ve researched and not personal experience. You can take the public ferry from Sorrento or from Naples. Maybe Naples is more convenient for you. Once in Capri, there are lots of options in the marina to take about one hour tours around the island. Maybe you have time for the Anacapri chair lift which is supposed to be fantastic.

Where are you staying?
This site is great for ferry schedules: https://www.sorrentoinsider.com/en/ferry-schedule

We are staying on Conco Marini
We will have a car and thought we might drive to Sorrento and park to use ferry or a more private tour.

Sorrento is probably your best bet, but there are more limited ferries out of Amalfi and Positano, so I would check that too.

Best is subjective. We took a shared tour of Capri from Sorrento with Mondo Guide.
https://www.sharedtours.com
We felt this was the BEST way for us to utilize our time (one day) to see all the major sites on Capri with a minimum of transportation planning and hassles. Well worth it to us. The cost is per person and is a shared group tour - minivan and boat around Capri.
We met our guide at the dock in Sorrento. The group assembled. We took the public ferry over to Capri (included in the cost of the tour) and then boarded our private mini-bus to tour the island,- Capri and Anacapri, then later we boarded a private boat around the island and made the stop at the Blue Grotto. The tide was too high and the waves were rough, so the Blue Grotto was closed, but that's the chances you take. Still the boat ride around Capri was worth it.

Can you DIY? Yes.
The cheap way would be to take the public ferry from Sorrento to Capri harbor.
From the harbor, you'd have to figure out a way to up to Capri. many use the funicular or take a bus or a taxi.
From Capri, you'd want to visit Anacapri. I think there's a public bus, but you'd need to research this. Or take a taxi
At Anacapri, you may want to take the chairlift up and back.
Then you'd need to take the bus or taxi back to the harbor from Anacapri.
and book a boat ride around Capri. The Boat will stop at the Blue Grotto.
And if it's open, you will pay additional fee to transfer to a small rowboat, which takes you into the grotto.
Then back on the boat to Capri harbor.
Then you would take the public ferry from Capri harbor back to Sorrento.

I would price the cost of catching all the separate transportation elements and then compare the cost of the guided tour per person. Balance the hassle factor of DIY and decide if a guided semi-private tour is worth the cost. Our guide was excellent we learned so much more about Capri than if we DIY'd it.

My current plan is to drive to Sorrento to park and take the early
ferry across.

First question would be in what season? Driving the coastal road during busy high season is reported to be a real headache. As well, in the past few years there have been some restrictions based on even/odd plate numbers. Last year's details:
https://distrettocostadamalfi.it/wp-content/uploads/2023/04/Distretto-Turistico-Costa-dAmalfi-Traffic-Regulation-in-Amalfi-Coast.pdf

You'd do better, IMHO, to ferry to Capri from Amalfi, Maiori, etc, with a port closer to your accommodation (full schedules for spring are not up yet). Ferries are the "public boats" and they travel directly to the Capri port, not a sightseeing route "around" the island. Anyway, you can easily explore the island on your own with some reading in advance (we have).

https://www.capri.com/en/t/amalfi/capri
https://www.capri.com