This is coming from experience. You should DEFINITELY start with a stand up martial art because grappling requires you to get up close, so start from a far distance martial art and then build up closer. You get what i mean right? Here is an example of what i mean.
Start with:
1.)Taekwondo
2.)Thai/Sanda kickboxing
3.)Judo/BJJ
You can skip taekwondo but it is truly the best far distance martial art but it lack close up combat.