According to the Oxford style guide, these are the appropriate titles and the order in which to use them:
Postnominals
remember that you do not need to list only all awards, degrees,
memberships etc held by an individual – only those items relevant to
your writing
the order for postnominals is
civil honours
military honours
QC
degrees, in the order
bachelor’s
master’s
doctor’s
postdoctoral
diplomas
certificates
membership of academic or professional bodies
do not include a BA for Oxford/Cambridge graduates if they also have
the MA give the name of the awarding university (using a shortened
form if required and if easily recognisable (Oxf, Camb, UCL etc) if
academic qualifications are relevant. A space is used to separate
degrees from the same institution, and a comma is used to separate
sets of degrees from different institutions; if the same level degree
has been awarded by more than one institution, list them in
alphabetical order of institution
Professor Xavier Postlethwaite, QC, BEng PhD UCL, MA PhD Camb, MA
DPhil Oxf, PhD Manc, FRS
Sir Charles Overlord, VC, BA S’ton
I would not use anything lower than a PhD when signing a letter. It is inappropriate in most countries, definitely in the US. Other titles including P.E. and and political titles are also acceptable.