I've been helping companies succeed online since 1995. I've seen it all. My focus areas are helping companies utilize the internet and surrounding technologies to market more effectively and integrate efficiently; business strategy; and technology strategy.
I tell my clients to think of their websites like a sales funnel. Try to look at each step of the site as a step in the funnel. You want to shorten that as much as possible but still give your potential customers the information they need to make the informed decision you want them to make.
Secondly, you want to test, test, test. There is no silver bullet here. By setting up an A/B test process on each of your pages and on each element of the page, you can test every aspect over time and optimize to get the best results for your website. There are some really easy ways to do this now. So, whatever you start with, do the testing and improve it regularly. Make testing, evaluating and improving an ongoing part of the process and you will get the conversions you want.
Without knowing much about your podcast or ultimate business goals here, I would say reaching out to the potential sponsors to at least get a feel would be a good idea. You might even consider some promotional sponsorship rate for one or two sponsors to get in early. If you have a marketing plan to show how you are going to work to drive the traffic necessary to make their sponsorship worthwhile, then they might be willing to take a chance on you early. Rewarding them for taking that risk with a slightly lower rate could be good for both of you. Good luck and enjoy!