@arthur Raising a series A type round (2M and up) will be extremely difficult without either great metrics, an A+ team of people who have killed it before, or a technology that will dominate a tech industry.
To be honest, raising an angel round of $500k isn't a fast/easy process either without some good metrics or someone behind you who believes in the vision. Likely a few month process if you can get in front of the right people. As you said you are looking for someone with connections this may take longer.
I think, as @sanjeev said, figure out your next key milestones (user adoption, retention, revenue), and raise enough to hit those targets. Likely you want enough to be findable at series A. So how long will it take to show real traction, etc. How much money do you need to get there. Add 33% because you'll underestimate. Sell the vision.
Also, I'm not exactly sure what your company is/does, but you should spend on the biggest risks first. So if your biggest risk is getting the tech right (think a company like Occulus), then spending the $500k is reasonable. If the biggest risk is that you haven't proven the need or that you can capture a large market (mist likely in a marketplace), you should be spending on proving that given a solution you can bring in tons of users. And if it's business model focus on showing users will pay and your costs (cac, unit costs) can generate huge profits.
Good luck and hope that helps.