To be honest, you get what you pay for and the budget is not that high. I set up a web site for a relative recently and used Zen hosting, based purely on my experience of them being a decent ISP. I think it was their £3.99 a month package. It works well enough and was hassle-free to get up and running.
I'd expect any hosting at this level to be on fairly well-thrashed hardware so don't expect it to be lightning quick or for support to be that good.
For that reason, just make sure that you get the domain registered in your name and have the facility to administer it online, so that when/if the provider becomes a problem, you can move elsewhere quickly and easily. Consider hosting the domain name elsewhere for this reason. Also, make sure you back up everything at the hosting provider's site regularly. I have had accounts at this price point where the databases have just disappeared overnight when they've screwed up an upgrade and all you'll get from tech support is a shrug of the shoulders.
I'd consider using a popular CMS or basic LAMP stuff if it's just going to be a simple site and avoid anything Microsoft specific, as this will give you more options if you need to move it IMHO.