If I want a third party to handle it how much should I pay them to handle my adwords account? Say I want to spend about $300 a month on advertising, what would their markup be? I assume they would report back to me weekly with an analytics report. Is that extra and how much do they charge for that?

Most pay per click management companies charge about 20% of the budget.

You can negotiate a lower percentage, depending on how extensive the work you want them to do and what you can do yourself — create your ad, test your ad, develop all your keywords, track the clicks and costs and adjusts the campaign accordingly, set up your Google Analytics account to track the performance of the campaign