LM3 feels like a fusion of 1 and 2, combining the key components of both.

I really need to get around to replaying LM1 someday, haven't touched it since 2010, don't even know a copy anymore.

3 for me, combines the strengths of 1 and 2 plus its own brand of flavor and originality and creates an almost perfect game.

I've been taking my time with 3. So far I'm at the shopping center floor (pretty early on). If the game keeps up like this, it will easily be my favourite in the series.

There's some really amazing floors ahead of you. (And one or two meh ones, but the majority are great)

I loved the first. Own but never played the second. Want but haven't purchased the third.
My opinion is invalid.

The first had the best atmosphere and controls.
The second brought a lot of innovations to the series and brought it to a lot of players.
The third smoothed out a lot of problems of the second will having some design callbacks to the original game. I don't know where it will rank in the long run, but right now I say it's the best. I smiled many times in the game, and it made me feel like a kid again.