Welcome to the area. When I moved here I didn't know where to start either and just started digging around. The ponds in town are a great cheap trick, a bucket, couple rods and a spud to open up old holes was all I used to have here when I didn't have room to store my shack and stuff starting out in a 300 sq/ft Bozeman mansion. Perch and trout in Glen lake (Bozeman Beach, the one by Map Brewing) was where I went when I didn't know anywhere else to go. The one behind the mall and lakes over off Davis have panfish in them. Hyalite is a good time for trout, just make sure you have your poop in a group going up there if the roads are slick. Traffic is bad on weekends and as soon as one car goes in the ditch coming out by Langhor it turns into a parking lot. I like to have chains in my pickup. The good part is there is always enough people going in and out up there you won't have to worry too much about being stranded. Be smart at the inlet (south) end of the lake, the ice can be crummy up there. Same with where the creek (Blackmore, I think?) comes in by the boat ramp. Cutthroat are deeper, brookies are up high. Look around Whitehall as well, but you need to have a capable vehicle. Canyon Ferry isn't a bad haul either but the fishing is hit or miss in my opinion and it can/will be a windy sucker.
We're the guys in a black Frabill suitcase shelter with the loud old Earthquake gas auger and are pretty friendly guys if you stop by and say hi.
