I found an ad in the classifieds from a company looking for someone to build them a webpage. I emailed them & told them I can build them a website & advised them that currently I only have adult sites to show them as samples, therefore samples will only be shown upon their consent. They responded back stating they are not looking for an adult site,

, that it is for a medical provider. So, I responded back that I will create a sample site, which I did, & emailed them the link.
This morning I had an email with some of the info to begin the site. The job only pays $200.
The part I need help with is the logo. I've been messing with FireworksMX trying to make one, but they look shitty, so I was thinking I can have someone else make the logo for me.
This however presents a problem of its own. I am broke. If anyone is willing to make one cheap, on my word that I will send payment when this DR's office sends me the check, I would greatly appreciate it. I estimate that I could finish this project for this company within a few days depending on how fast they send me the information they want on the site, & on how fast they send any images, links, etc & also completion time would depend on if they require revision, change, etc..
I never designed for anyone else other than myself, so I assumed I get paid after I am finished, or do I ask them to pay me upfront? If they pay me upfront, then I suppose I will just pay for a logo immediately, but I need inexpensive & quick.
Here's another thought. When dealing with potential paying clients over the internet, & requesting payment in advance, what is a good way to assure this company/person that I will deliver the goods? Obviously I am going to give my name, add. ph#, but should this be enough?
any suggestions or advice is greatly appreciated.