The series is best thought of as being split into multiple generations kinda like Pokemon, with the numbered entries being the start of each gen and establishing new rules and systems for following entries. The in between titles are treated more as stand alone expansions, where you can technically start with any of them, but they are designed quite heavily with the expectation that you played the numbered title it's based on, because often you can transfer your save data from one game to the other. Credits and AC parts primarily.
So you have 1st gen, consisting of all the PS1 games (AC1, Project Phantasma, and Master of Arena), followed by 2nd starting on PS2 (AC 2 and Another Age), 3rd Gen (AC 3 and Silent Line), 3.5 (Nexus, Nine Breaker, and Last Raven), 4th Gen starting on 360/PS3 (AC4 and For Answer), and finally 5th Gen (AC V and Verdict Day).
Each of the games have their own missions, structure, features, etc that they aren't considered updated rereleases, but rather a new package of content to carry over your data where it is applicable. Because of that, it's honestly best to start from the beginning with the PS1 games. It's simple relative to what a lot of the games later would become, and from beginning all the way to the end of the PS2 the series is extremely incremental in its iterations that prior experience is almost required at a point.
Of course, whether or not you wanna go the whole way and complete every single game like I did is another matter. If I had to narrow down the generations that are must plays, it's 1st, 3rd, and 3.5. That's 3 PS1 games and 5 PS2 games, about more than half of the total mainline games. Maybe check out 2nd and 5th gens if you're curious, the latter is quite different in a lot of respects but well designed in its own right. Only games I'd say to outright stay away from are 4 and For Answer due to being so bleh and unfocused in design.
