Suwalki, in 1850-60, was not only a city but also a gubernia or
administrative district. It was more common, at that time, for
Jews to live in small towns-so he probably lived in a small town
in Suwalki gubernia rather than the city. Suwalki, the Kingdom
of Poland, and Lithuania all belonged to Russia. The only border
in the area was the Prussian border. Suwalki gubernia covered the
northeast of today's Poland and a little Lithuania, so it would
cover the area he was from.
Since they say he was born in Suwalki, it was not Prussia but
Russia. I heartily recommend checking for birth records in JRI-PP
because you don't know the exact town for sure (it may be the city
of Suwalki-or maybe not).
In addition to the LitvakSig, there is a Suwalki-Lomza Special
Interest Group which is not online but has a journal periodically.
They have a lot of additional records for the area, and you might
want to join that as well.
"My question is this...for the year 1850-60, when this Julius Lewis
Myers was born, as a border town, do I look in the Polish Records
for Sulwalki or Lithuanian records, or if it was part of the Russian
Empire as a whole where do I then search?"