Congrats on starting a fun journey! I'd say it depends on many factors but some quick generalizations:
- Build everything gradually . . . don't get injured by doing too much too soon, or going too fast too soon
- Do you currently swim? As long as you can comfortably swim the race distance, I personally would probably want to be swimming 2-3 times a week and just be working on being very comfortable with the race distance
- How about your biking? You want to ride enough that the race distance and any hills etc. will be no problem on race day
- At some point you should try a "brick" workout (running after biking). You can probably save this until after your 10K. But you want to do it a few times before race day. It usually feels pretty weird trying to run after biking, and doing it a handful of times before the race will help you adjust.
Mostly make sure to get enough rest, be consistent from day to day and add only a little bit of time/distance per week. Mostly have fun with it, you're going to learn a lot!

I've been swimming enough that the distance is super easy now, I'm not particularly fast though (2:10/100 yards). Biking wise, my ftp is a little over 300 and I'm super comfortable there. The run is really my main concern, I'm comfortable running a 5k, but I'm extraordinarily slow. I know losing weight will help and I'm dropping about 1.5 pounds a week.

Sounds like you can just pretty much stay with what you're currently doing with swimming and biking and mostly focus on building up running volume (gradually). You sound well suited to tri, with being comfortable in the swim and bike already. Continuing to do those can also help you with your running a bit, acting as recovery workouts for your runs and allowing you to do more overall volume than just running alone. Have you looked at the Barry P running plan? I think it is very effective. If you aren't already, I'd start doing one "long" run per week. Say you can currently do 3 mi (very easy pace). Next week you might go 3.25, following week 3.5 etc.