I do not have a Commando, but my main is a Mercenary. I levelled using the Arsenal tree (The mirror of Gunnery for a Commando) up until 40, where I respecced into Bodyguard (Combat Medic to you).
Levelling as a healer is much slower in my experience, so if you want speed, then your best bet is to level as a DPS. I personally find levelling healers more fun, and it also allows me to get used to new abilities from a healing point of view one at a time, rather than having to figure out everything at once.
This is a basically the build I use on my Mercenary, only in a Commando skill tree. There's not a huge amount of room for change within it really, but if you wanted to have a play around with it then you could take the 2 points out of Weapons Calibrations and put them into something like Cell Capacitor if you don't feel confident enough in keeping your heat low. Alternatively, for levelling purposes, you could benefit more from moving the points from Weapons Calibrations into Efficient Conversions and Combat Shield. That way, you've got a few bonuses for a bit of control without using heat and you can always pop your shield and carry on healing if your tank companion messes it all up!
From an end-game PvE sort of perspective, I'd highly reccomend the build I posted. It's pretty much got all the bread and butter skills and talents for the Commando healer, so you should be good to go with that
- Take a look at that build, it's really good for an end game PvE Combat Medic. Leveling with Gunnery or the other DPS tree (forget it's name) would be faster than leveling with Combat Medic.