I have recently come into a collection of records, albums 78's waltz foxtrot to Beatles and was wondering who the best person is to sell to to give me an honest price.
depending on their cash-flow^W trickle situation, a reliable dealer will give around one third of the price they expect to be able to get for those discs as are listable;
listing them yourself (artists - a/b titles - labels - cat#s - condition estimated by eye) will likely get you the best price overall, but is time-consuming, and they could take quite some time to shift (via e.g. eBay);
half-way house: list as above in batches by individual artist, give average condition for each batch. . .
Well, depending what you have, some Beatles records can still be worth a few bucks. Just read around Ebay (completed listings tell you the actual selling price).
with regard to 78s local shops seem to want 50p to £5 for average ones. But the dance bands / jazz do go for more. So you need someone with money, (and space and big muscles to shift them)
What country/town are they located in ?