Very sorry to hear. I had a prop strike (pothole during taxi) in 2002, with just 1 hour on the clock... I am quite careful with grass these days, as a result. Not because grass is a problem but because it tends to go with a "lesser" attitude to airfield maintenance.
Can/should the prop be repaired ? There doesnt seem to be any damage to the tips only a slight bend.
An engineer should give you the legal verb on that but you should not do it. Change the blade. If a piece of a blade comes off, you will definitely know about it, and the engine could come off rapidly, very soon afterwards.
If the prop needs to be replaced is it worth thinking about a 3-blade model? Any idea of the rough difference in cost?
Depends on the prop. Quite a lot of people have done that. There is unlikely to be a perf improvement but it looks a lot better
However, the Hartzell 3B props have a tougher rule on prop strikes than most 2B props. From vague memory, if you have to remove 2 or 3 blades for any reason (for repair) then the hub has to be scrapped, and economically this means they sell you a whole new prop
In my case, the prop was £11k with a JAR-1 form, or US$9k with an 8130-3, and the latter was perfectly fine for the G-reg it then was. But the word "insurance" means much the same in aviation as in the car trade i.e. everybody rubs their hands. I got the £11k prop...
You will have to NDT the hub anyway, even if you fit 2 new blades. Plus overhaul the governor (which includes an NDT of that too). Plus overhaul the magneto(s). All these bits can get shock loaded.
The engine is 10 years old and has just over 600 hours on it. Should we consider using this as an opportunity to have the engine zero-timed?
I would say No but it depends on its condition, obviously. They will let you know how good/bad it is when they open it up and strip it all down for NDT, anyway.
They may find corrosion. 600hrs in 10 years is plenty of hours but also
could mean some long standing around.
Anything short of an "overhaul" is a "repair".
Anything else we should be thinking of?
Use a competent engine shop, not the usual cowboys which dominate the UK scene

I sent my engine to Barrett Precision (for the
SB569 job) which is perhaps the most reputable shop in the USA but you can't do that if you are on G because BP cannot issue a dual-released 8130-3. You will have to use some UK shop, or one of the bigger US ones like Pen Yan, etc.
Make sure the shop knows about balancing the weights, etc. A pilot has just emailed me to say his engine was rebuilt and is shaking quite badly; 0.8 IPS on the dynamic prop balancer which is verging on unairworthy; I guess they forgot to match up the opposite pistons / conrod small ends or whatever.