One of the best introductions to 18th-century letter writing is that by Frank Baker in Vol. 1 of the edition of John Wesley’s letters. Wesley was a Methodist minister who lived from 1703–1791, and he was a voluminous letter writer. There is a collection of letters from his hand available online called the Letters of John Wesley at Bridwell Library. This is a digital collection which presents 138 letters by Wesley letters, in the form of scans along their transcriptions. According to the website, these transcriptions are fully searchable.
Baker, Frank (1980), The Works of John Wesley, Vol. 25, Letters I, 1721-1739, Oxford: Clarendon Press.