Personally, am not enamoured of swopping chucks between backplates. But, at the moment, this will get you going, and then you can search for a suitable backplate for the 4 jaw in a more leisurely way. By then you will have gained enough skill and confidence to undertake machining the register between backplate and the 4 Jaw chuck.
There's been a first time for everything, for every one of us!
Agree with the advice to buy screw thread gauges, (for Whit, Unified, and Metric threads). In the future, you will find them invaluable.
As a newcomer, DO try to find a Model Engineering Club near to you, and join. You will get a lot of help and advice, and companionship, (or you should if the club is any good). One day you may need, for a once in a lifetime job, an oddball Tap or Die, and someone will be prepared to lend it to you; or to give practical help (their shop or theirs) with a particularly difficult problem.
I can vouch for being made welcome when visiting other Clubs. Next season, (I think that you are near Gloucester?) Visit Hereford S M E at Broomy Hill. You will be welcomed (Living 140 miles away, I am not a member, and The WaterWorks Museum is next door, and worth a visit. Very occasionally, I volunteer there).
Hope this all helps
Howard