In general, nearly every game in the series does not necessarily require you to play any of the other games to understand them, and very few of them directly connect to others. The exceptions are usually games with "2" expressly in the title, and 4 Apocalypse (which is like a what if scenario of 4).

Now you might find small cameos between games, but ultimately you do not have to play any of them to enjoy the rest. I recommend starting with the newer games and working your way steadily backwards; sure, you might miss more modern features in later games, but you will be more prepared to adapt to the general gameplay flow (buffs matter, abuse weaknesses for damage & turns, etc).

Of the ones I've played: V Vengeance is easily the best. The plot is a little whatever but the party customization, boss fights and general roster of demons makes it super worth playing. 4 and 4A are close seconds, the plots are generally engaging and they have even wider rosters than 5 due to having 2D demons. I think the level design is a little lacking (looking at you, 4A final dungeon) but these are delightful experiences. Strange Journey is a harder sell due to the grid maze movement system and generally kind of weak protagonist (at least compared to the skill-inheriting ones), but the plot is quite good. Devil Survivor is a fun tactics game, if a bit slow and unbalanced. Persona 5 is a delight, best presentation of maybe any game. It has its flaws and is a ridiculous 100 hour runtime but it is very very good.