Consider starting with the TOS movies. They're a great introduction to the original cast, using a higher budget and better writing than the show. They're set after TOS, but don't require you to know anything about it to watch them. The quality of the movies follows the playground rhyme "first the worst, second the best".

My personal favourite series, by a country mile, is Lower Decks. You are in for an absolute treat whenever you decide to start on them. Unlike the others, though, Lower Decks massively rewards familiarity with other Star Trek series. The more of them you watch before picking it up, the more you will get out of it.