Don't bother with the open worlds early on. Instead focus on making progress on the starchart.
Farm Rhino, then focus on working twords the resources needed to build him. Even if they like their starter, having a second option in a few days is really nice.
The basic Vectis is a very good weapon for new players.
Do Spy missions and void missions where possible. Void missions for all the sweet mods that drop from some of the containers and spy missions for other mods, in particular base damage mods and dual-stats. For a new player getting a solid suite of basic mods quickly is pretty critical.
If you are playing with your friends carry one poorly modded weapon and one good one on a support frame of some kind. Use the crap weapon most of the time and keep an eye on your kills (tab) so you don't get ahead of them. Only use the good weapon if things are going badly to salvage the situation.
As for what frame to use: Oberon with Phoenix Renewal is pretty good, as is Wisp if you only use your health buff. Trin is another great option since you can also give them energy. Basically it sucks to die so just being there and keeping them alive can make things a little easier. Trin is arguably the best new player carry frame because you can top off their energy and therefore let them use their abilities more.
Be very careful using your operator lest you spoil things. This is a reason to use Oberon actually, you probably hop out into your operator to revive normally, but with a new player or two you probably don't want to do that so having a frame that is on the tankier side doesn't hurt. If you are fast you can probably use Zenurik without anyone catching on, and if they do see a flash of operator in void mode you can probably just wave it off as a ability they unlock later.
See also:
Brozime's latest FTP run. This is a series of a experienced player starting over with a new account to get a feel for the new player experience.
Week 1Week 2Week 3Week 4Week 5(linked videos are the recaps, full stream archives are also available if you have huge amounts of time)