I am a search engine marketing consultant. Have been using SEO and managing PPC campaigns for 15+ years. One of my current Adwords clients is an app creation client. I know the space quite well. Here is my advice:
1) $1k/mo will get you very little results unfortunately. Your best bet is to front end the first month with more budget, because you need a certain volume of data before you can make INFORMED decisions on whether it makes sense to continue and/or how to improve your Adwords campaign performance.
2) do not ignore bing/yahoo network. Some of your competitors do ; ) Generally your CPC will be lower there.
3) be smart about when you advertise. Performance on weekends and late night generally is diminished.
4) 7-10% conversion rates? Not happening. I would expect max 5% in your niche.
Organic SEO is a better long-term approach, IF you can achieve top 5 rankings. I personally would run adwords for a month or two, determine ROI... and if not feasible, move your budget to proper SEO, content development, and link building.
If your budget is limited, PPC ads aren't likely to give you the biggest bang for your buck. I'd suggest a more organic approach to getting customers.