if you're on FindmyPast, you can access scans of many, but not all, parish records from Wales. The records have recently gone onto Ancestry as well, but their indexing leaves much to be desired, which makes searching the more common surnames a bit of a task.
If the parish record of a marriage is available after the start of civil registration, it could save you the cost of the marriage certificate as there will be no more info on the cert and the scan of the register should have the signatures which a certificate from the GRO doesn't.
I'm not finding baptisms for William & Anne's children so the family might be non-conformist by that time.
1861 census for William's parents & siblings at Cwm Breinant
https://www.familysearch.org/ark:/61903/1:1:M7CF-L8Whttp://www.rootschat.com/links/01q67/1841 at Rhydgoch
https://www.familysearch.org/ark:/61903/1:1:M7QR-KR9http://www.rootschat.com/links/01q68/Checking the birth registrations for children with less common names
Francis Thomas dec qtr 1843 Llandilofawr vol 26 pg 549 mother's maiden name Thomas
Possible marriage in Llandeilo 15 March 1833 for John Thomas of Llanfihangel Aberbythych and Ann Thomas of Llandeilo, witnesses David Thomas & John Harries, all signed.
Possible baptism for William in Llanfihangel Aberbythych 9 June 1833 son of John Thomas, farmer, and Anne of Gellyfawr.
