I enjoy the whole franchise. I can see where many don't care for Rambo 3, that was actually the first and only Rambo movie I saw for a long time, it was the newest when I was a kid and they aired it on TV back in the 80s when edited for TV really meant something so it was like PG, PG-13 level by the time they were done. I also grew up on the old cartoon and had the toys from it, so I grew up thinking of Rambo as the shirtless guy with the bandana kicking ass. When I finally saw Rambo 2 I was excited because now he had the red bandana like the cartoon lol. First Blood was the last one I saw, I wondered for awhile why he was in jail at the start of 2. Back then it was just VHS and not ever shop had every movie in my small town so it was a hunt, eventually I got tapes of all 3. For a long time First Blood didn't do much for me, it wasn't Rambo as I knew him, that was the odd movie and 2 and 3 were Rambo. As I grew up, I came to admire the quality of it as a film and see the character as one over the whole series.
My absolute favorite movie in the series is Rambo, I just love his character arc in it, the music, the action, it's a great blend of action from 2 and 3 and story from 1. After that it's Rambo 2, just love everything in that movie, the knife's my favorite of all, his look will always be the iconic look for me, the music was great, the action was perfect. After that I'd say 3 and then First Blood. Again, I will give First Blood credit as being the best crafted of all the movies and number 1 in that regard, but it's probably the least overall satisfying for me as I came to be a fan of the series. Had I seen that first, I might feel totally differently but this is how I came to know him. I'm the same with Rocky, I grew up on Rocky 3 and 4 and those left distinct marks on me so by the time I saw 1 and 2, they felt very strange to me and somewhat boring at times. As I got older I grew to appreciate them and that's why Rocky Balboa is my favorite, it has everything I love from the series in one film.