Dear anonymous. Broad audiences, beta versions, and QAs are for big companies, not for startups - you don't need any of that, or investors for that matter (if you do, then you will not find them).
The best (if not the only) thing you can do right now is to narrow down you audience, choose just one segment, and start marketing your app.It
doesn't matter at all if your product hasn't passed QA.You think that your product is universal enough to fit everyone, but it's not, never is. Don't worry about your small infrastructure - you are highly unlikely to get more than 1K users any time soon, and even if you do, having your servers crash because there are too many users is by far the best story you can tell the investors - they love hearing stories like that.
Seriously though, before you even start looking for investors, you will need at least 3 things:
1. Real traction (in terms of MAU or interaction units, or whatever). How many depends on the product, but for a "free app" I'd say no less than 10,000 users, but preferably 100,000, and growing at least 50% per month for at least 3 months.
2. A validated business model (unless you have millions of users - that might look like a short track to exit before you exhaust the investment money). You will have to implement your monetization feature and measure it, i.e. what is the LTV (life-time value) of each user.
3. A proven user acquisition strategy with precise estimates on how much it costs to acquire each user (it always does), i.e. CAC (customer acquisition cost). LTV must be at least 3 times greater than CAC for it to be interesting.
Without all this, going to investors is a total waste of time (and worse), unless you're a shark who's already done an 8-9-figure exit recently, so you can raise money based on your reputation alone.