Which woodwind instrument should i play? (tenor sax, clarinet, alto sax, or baritone sax)?

Most people who are beginners in band tend to start on either an Alto Sax, or a Clarinet (Out of the instruments you suggested) I played Alto sax for 3 years of band then switched to Tenor for a year, and then to Baritone which I've been playing for 5 years. It's a great way to slowly go down in instruments (if you want to.) One thing you have to remember is the bigger the saxophone gets, the more air it will take to play. That is why I suggest to start on Alto, so your lungs can become stronger before you try playing a Bari. Another thing you should consider is what types of parts you will want to play. The longer you play an instrument, you will see patterns in what types of music parts the instrument gets. Alto tends to get a lot of lead parts, with melody, but along with that melody, comes tricky rhythms and fast notes, meaning more difficult parts that you will need to practice. Baritone gets parts similar to what the Tuba gets. Lots of quarter notes and keeping the beat for the band and getting melody is pretty rare (though it does happen). there is the occasional eighth or sixteenth note runs, but not nearly as often as the alto. The tenor is right in between the other two. They get melody occasionally and do a lot of harmonizing. I have never played the Clarinet, but I have heard it is more difficult than the saxophone to start on.

Take some lession on the Alto Sax gospel Alto saxophone above all

I say alto because once you learn that, all the others will be easier to learn later.

I think the best way to decide is to try them all out. If its possible have 1 lesson with each, call up some teachers and ask them if they would be willing to give you a first lesson using their own instrument so you can decide whether you like it or not. If not go into a music shop and try them out, Im going to assume that you dont know how to play, so just try it out for comfort (like the size and weight of the instrument) and ask the assistant if they know anything about the instument like the finger and hand positions and see if you are comfortable and confident holding it that way. To be honest though, you get used to whatever instument you play with practise so dont worry if you dont find any of them that comfortable. Also listen to some solo performances of all the instruments and see what you prefer to listen to. With the instruments you have listed there might not be too much difference but there is still a difference. Whichever sax or clarinet you pick, remember they are in the same family so if you decide after a year that youd prefer to play another one from the family, it should be an easy change to make.

alto is a good start.