For practical reasons I am focusing my Melrose one-place study on the pre-1820 period. Later records such as census returns and civil registration records have been heavily transcribed and indexed already, and indexes and digital images are readily available at websites such as ScotlandsPeople.gov.uk, findmypast and Ancestry UK. I see no benefit in my reproducing the excellent work they have already done. I can make more of a contribution by focusing on the earlier period.
Church of Scotland parish registers before 1855 for Melrose are also indexed already, so I will not be reproducing that here. The indexes are freely available now on ScotlandsPeople with links to pay-per-view images of the original records. In addition a transcribed version of some of the parish records was published at Edinburgh in 1913 by the Scottish Record Society. Edited by Charles S. Romanes, and entitled Melrose parish registers of baptisms, marriages, proclamations of marriages, session minutes (1723-1741) and mortuary rolls: 1642-1820, it contains baptisms, marriages and burial records, together with a useful index of names for easy access, including names of mothers of children, baptism witnesses, cautioners etc. This out of copyright book has been scanned and put online by the Internet Archive.
For early maps of the Melrose area please visit the National Library of Scotland’s online map collection. Their digitised maps include John Wood’s 1826 town plan of Melrose, earlier maps of the area, and later Ordnance Survey ones, including large-scale.
Also worth visiting is ScotlandsPlaces.gov.uk which includes many digitised tax records, especially from the 18th century, and other resources such as the Ordnance Survey Name Books from the 1850s which include detailed information about the history of specific places in Melrose parish as remembered at that time. For early place names it is also worth checking the National Library of Scotland’s place name index for Blaeu’s atlas of 1654. It includes some place names not recorded on later maps.
The Melrose pages in GENUKI (the UK and Ireland genealogy information service) contain information about numerous local genealogy resources. In a similar vein the Borders Family History Society has a very useful Melrose page, which also includes details of the many local genealogy publications the society sells.
The Scottish Borders Archive and Local History Centre in Hawick holds numerous local records, many not digitised. They include school records, parochial board minutes and accounts (later poor relief), local crime records etc. They are well worth checking out.
Finally, especially if you are local to the Melrose area, or visiting, I recommend checking out the Melrose Historical & Archaeological Association.