Cherokee Purple and Brandywine are two of the most well-known heirlooms out there and they have become readily available in recent years. They both have excellent tomato flavor. I've grown them for several years, though not very successfully the last few. They're more challenging to grow than hybrids because they're not bred for disease resistance, early ripening or high yield. They're finicky.
If you spend some time searching the net for ideas on heirlooms you'll eventually run into a contingent of heirloom snobs that will drone on endlessly about Glick's versus Sudduth's versus Cowlick Brandywine and dozens of others. Skip that crap. I'd advise getting a few heirlooms you can find locally and take good care of them. I think our beloved billethead grows an heirloom or two (maybe Black Krim) and we all know his tomatoes are bigger, his lettuce is lusher, his turkeys are plumper, his wok has more BTUs, etc ?? in fact, disregard the above and just PM the man.