They get better as they go along (with the exception of Absolution), so my list is basically the same as everyone else's here.
Hitman / Hitman 2
Blood Money
Contracts
2: Silent Assassin
Absolution
Codename 47
The first game has too many levels with outright incoherent, nonsensical solutions (see the bizarre ways you have to get into the drug lab in the drug lord's compound or how you get past the checkpoints in the harbor). If the game had mid-mission saves instead of the awkward lives system, it'd help ameliorate that, but as it is it's just annoying to play. As another poster in this thread did, though, I have to give a shout-out to the hotel stage, which is genuinely great - shockingly so, given the rest of the game - and is in some ways cooler than Contracts' remade version.
The original Hitman 2 is cool but there's definitely a lot of awkwardness in the way you have to tiptoe around guards at all time to keep your disguises from being blown. I like the game just because I love the core Hitman concepts so much, but it has a few very unpleasant sections and is genuinely a clumsy game.
Contracts is the first great game of the series. There's a tiny bit of 2's oddness but it's mostly smoothed out. I don't think it's much weaker than Blood Money, honestly. (And of course Blood Money is stellar; there's not much to say about it.) I do take some issue with the fact that the game doesn't have many unique levels and that some of the Hong Kong levels from the original game don't feel especially enhanced (this also makes the difficulty curve of the game odd since the last several stages of the game are just Codename 47's intro missions) but it's still great. I actually appreciate that it's easier for enemies to see through your disguises than in Blood Money while not being as obnoxious about it as Hitman 2, because Blood Money is too generous in that regard.
Blood Money might be the most overall balanced game in the series, if only because the modern games need to be finagled with a bit, mainly just to turn off some of the in-game guide stuff, before you can get what's great about them. In some ways I don't like how much easier Blood Money is than its predecessors but it's clearly one of the best games in the franchise despite that, full of cool level concepts. I think it has the best overall ambience of the series too; its music and sound design trump the newest games'.
Absolution is kind of lame. I don't think it's a bad game, but what it does (which is mostly traditional line-of-sight stealth obstacle courses) just isn't what I come to Hitman for. Codename 47 is almost inarguably a worse game, but I feel like I'd rather replay it than Absolution.
Modern Hitman is, of course, a masterpiece. I do have some complaints, though. I think the mission story / opportunity stuff is way overbearing, and if you don't turn it off - ideally all the way off - it really hampers the experience. (If I had to make a ranking, I'd say modern Hitman without assistance > Blood Money > modern Hitman with assistance.) There's an element to how the huge levels are set up that changes how hints have to be communicated to the player, too - again, I think modern Hitman is overall better, but I like that in Blood Money you're left to look at the environment and learn things on your own, whereas in modern Hitman there's a lot of listening to NPC dialogue or Diana hints even if you turn the hint systems off. And I don't think the mastery system is very interesting; it encourages rote checklist-like play. That said, best games in the series if you turn down the "modern" features and play them like you would the original games.
I've only given new Hitman 2 one full 20-hour playthrough, so I don't feel I can really judge it compared to 2016. It's at least around the same level, but it's hard for me to say whether it's really better or worse than its predecessor. I think I might like the first modern game's levels a bit more so far (with the exception of 2's Miami), but it's tough to say.
I haven't played Hitman 3 yet, but I'm sure it's great.
