Apple offer a 30 day free trial of FCPX, so you can see if it works for you without cost. No need for credit cards, no need to cancel, it just stops after 30 days. You still have any imported video though.
https://www.apple.com/uk/final-cut-pro/trial/
Hopefully you won't have any problems capturing the DV tapes into FCPX or iMovie.
Your Sony can record an analog input( VHS) to tape as you say, or signal convert it to the FireWire out.The signal convert function can be found later in your instruction booklet under the section connecting cam' to computer.
For the VHS tapes you might want to see if the signal convert function works first as you can go straight into the Mac rather than to tape first and then into the Mac. For this I would suggest you use the Record function in QuickTime Player as it probably won't import into FCPX or iMovie due to timecode not being present.
https://support.apple.com/en-gb/HT201066
If you cannot import VHS tape using QuickTike Player with signal convert then try recording to camcorder tape as suggested by Tom. This method should provide timecode, so you should then be able to transfer this into FCPX or iMovie.
You will need OS 10.14.6 or later to download FCPX ( trial or otherwise).
Importing tape based media ( including signal convert/pass through) appears to have become more difficult with the more recent OS's so if you are wanting FCPX then try the free trial first. 30 days starts the moment you first launch it, so be set up ready to go.
If FCPX can't import your media but QuickTime Player can, then you can still bring this into FCPX of course.