If you're only going with one, then yes, binos over spotting scope. The Forge 15x is an excellent value for the dollar, and I don't think you can go wrong by starting there, esp if you can pick up a used pair. Then you can sell them for basically what you paid if you end up wanting to step up, or to change magnification.
This thread (among many others, and I just saw another I can't find right now) has a lot of relevant discussion, read through:
new to the scene, looking to get more into LR shooting and eventually PRS series. Are most of you using binos or a spotting scope as optics on a tripod? why do you prefer one over the other? also, is 10X enuff on binos?
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ETA: I neglected to address your bino/RF combo question. I'd say that since you're on a budget and your main focus is competition, stick with your PLRF and get some decent binos. As long as you can get a stable platform for the PLRF (ideally a solid tripod mount) so you can be sure of your ranging reads, there's nothing wrong with that to get started with. Any reputable PLRF will be good enough for centerfire competition, especially when you're just getting started, and the main reasons to go with a combo setup in my mind are either cutting weight/bulk for hunting applications or simplifying co-witness when ranging targets. However, there's a pretty sizeable price jump when combining good glass with LRF capabilities, and I don't think it can be done well under $1k. The Sig 3000 BDX are perfectly fine for your purpose, but since you already have a LRF, I'd probably skip them in your case and just get the Forge. If you were gonna be hunting with the setup, especially in the West, I'd say sell your LRF and get the Sig 3000 BDX or really bump up into upper glass, but since it sounds like you're primarily competition-focused, your Forge 15x plan is rock solid. 15x is too much magnification for a do-it-all set of hunting binos, but again, for pure comp, lots of folks prefer the 15x.