I will list an effective Muay Thai combinations in this post. This time I'll will focus on Punch+Kick and Kick+Punch Muay Thai combos.
Most of them will be simple 3-count and 4-count combos that you can start using right away.
I have also added a few advanced combos and setups for more experienced fighters.
I'm writing them from a position of an orthodox fighter with a regular stance ie. left lead leg. You can easily adjust them for a southpaw stance.
Right low kick + left hook + cross [right straight punch] + left switch kick
Left switch kick + cross [right straight punch] + left hook + right low kick
Left hook + cross [right straight punch] + double left switch kick
Right low kick + left hook + right hook + left inside leg kick
Switch kick + cross + left hook + roundhouse kick
Jab + cross + hook + right elbow strike
Jab + cross + left hook to the head + left hook to the body
Jab + cross + left roundhouse kick + left knee strike
Jab + teep + fake another teep + quick jab and cross
And a more advanced Muay Thai combos:
jab + cross + left liver hook + left head hook + right head hook + left head hook + right roundhouse head kick
For a list of Dutch style combos take a look at: Dutch Kickboxing combinations.
Try them and choose the one that feels natural to you. Everyone's got different preferences. Most of the combinations start with a simple jab or a low kick. Some people like to start combos with a straight right punch - I don't.
At least not too early in the game. It feels like it opens up my guard too much and it neutralize my 'power punch' that I could use for a counter attack. I like to keep that punishing 'answer' for my opponent's attacks early in the game and open up later in the fight.
You can always do some more cocky strikes later on when the situation allows you to. Other people may feel different about it so you should try them before you decide what's the best strategy for you there. Try these simple 3 count combinations starting with a cross and check it for yourself:
Cross [straight right punch] + left hook + right low kick
Cross [straight right] body punch + left hook + right uppercut elbow
Cross [straight right] + left hook + right uppercut
Cross + left hook + right knee
And a more advanced combo:
Cross + left hook + cross + jab + cross + uppercut + cross
Also take a look at: