You're not going to beat the Doberman for your basic shooter drone. Putting just a fixed mount on another drone is as much as buying the doberman. Because the best dice tend to be from remote control, the typical weapon is one that is FA capable. The White Knight LMG is classic. I twitch a little at Forbidden, however, so I'll choose something a bit lighter. My personal preference is an Ingram Smartgun X with an ammo drum, and make sure the sensors have imagelink and smartlink. There are other good choices, too, depending on your situation and idiosyncracies.
I've begun to think I'm in the minority, but I always try to have an EVO orderly around. It's nice having a self-mobile ambulance gurney that's able to do the medic work so I don't have to while outrunning any unboosted and most boosted metahumans. I'll stick a first aid autosoft [3] on it and let it do the job so I don't have to. Oh - it always gets gecko pads, too.
Though you'll find plenty of arguments on the list as to whether it's possible, if you're going with the party but not doing anything significant, get a steel lynx and add a rigger cocoon. The arguments are on whether adding the cocoon is legitimate by the rules. Most tables say yes, but there are some well-run and enjoyable tables that say no -- check before you go there.
A common favorite is the LEBD-1 (from arsenal). Like the doberman, this does a lot for a surprisingly low cost once you look at the additions. If you've got This Old Drone, an alternative liked by many is the Lone Star Strato-9. (I've gotten tripped by the obsolesence so I'm not as fond of it , but it's still a solid choice.)
I like to recommend picking up two or three microtapper bugs (Unwired 198), giving all of them gecko pads and one of them 10 meters of optical cable. Put one on each side of a signal stopper and you've made a tunnel for your comms. One is all you need to turn a hardwired system into part of the unwired matrix.
I also recommend a handful of drones that are meant solely for looking around. Micros like the Kanmushi are hard to see, but they're very limited in how many sensors you can stick in there. The fly-spy, well, it's very hard to go wrong with a flying spydrone. I'm very fond of the dragonfly, especially since according to its verbal description it's supposed to have an ultrasound sensor built in. That particular issue is a gamemaster discussion, but at least you can point to the text.
Notice that I tend to go with cheap drones. I don't want to lose any, but I figure I'm going to lose a few. I'm less likely to be devastated at losing 5K than 50K
With that in mind, remember to prepare for that loss. At a minimum, remember that if you leave it behind there's a good chance it's going through a forensics lab. Self-detructs are outside chargen availability (darnit), so do what you can in advance: clean out the RFIDs, run cleansers on it before you go in, that sort of thing. If you can, bring them out -- it reduces problems from you forgetting to preclean your gear.