Now whilst you're more than welcome to contact me regarding the design of your new website, there are many many web designers out there who will be willing to help you - despite the fact that you are on a budget. The way to stop them recoiling in horror when you tell them your budget and time scale is to back it up with a few simple things which will help the design process go smoothly and swiftly and therefore keep the cost down.
Content is King - be king for a day...
Good websites need good content, it's a simple formula. If you are able to write all the content yourself then this will cut the cost down dramatically. Most designers charge by the hour, so an hour spent writing something that you could have written yourself is an expensive hour. A good designer will review your work, point out any things that need changing or re-working. Do yourself a favour and take this information on board, generally designers know what works in terms of copy (copy is just text) both in terms of readability, and search engine optimization (SEO). If you also have images ready then all the better. Don't feel you necessarily need the text and images up front, dummy data can be used during the design phase but the sooner the better.
Show Example Websites
Presumably you've checked out the competition right? If not perhaps you should, if there is none, then great! If there is (which there will be probably), do you see any websites that you like the look of? Pass them on to the developer, it will give him/her a feel of what you are aiming for (even if it isn't manageable with your budget). If there's any sites that you really don't like then feel free to chuck them in too. Most importantly, give the reasons why you do or don't like the sites in question. Try and be as specific as possible, saying "it looks pretty" is not as useful as saying " I like the way the menu is structured" for example. Being clear about what you like will help make the design process smoother and faster and ultimately cheaper :)
Manage Your Own Content
These days, most developers are familiar with using content management systems (CMS) so it shouldn't cost much more to incorporate it into your website (obviously this depends on your project). This way you can update the text and images to your hearts content (pardon the pun) without paying for maintenance fees, this helps take the pressure off the required quality for the content that you provide up front. You can refine it over time - the key point to remember is that you're trying to get something up and running, it doesn't necessarily have to be perfect just easily modifiable.
Be realistic about Timescale
If you're on a tight budget you need to be flexible, some developers charge a rush fee if they need to produce the goods in a real hurry, this is normally due to them having to stay up all night so it is fair enough really. I'm not saying it's OK for a simple website to take months or even weeks but don't expect it to arrive tomorrow! There are things that you as a client can do to help speed up the process, providing your own content as described above is one thing but also simple things like responding in a timely manner to emails from the designer - he/she will want your approval on designs or may need some extra details on something, if you don't respond to it for days then all you are doing is pushing back the finish line.
Take the hosting offered by the developer
Whatever your website does or looks like - it will need hosting. This can range between £5 - £20 a month for a single website. It's tricky finding good hosting but your friendly developer will have done the research already and if they are sensible then they will either be on a reseller program or like me will pay monthly for a virtual server. Having a virtual server means that they can host a large number of websites on a high speed service, if they have enough clients then the cost should be low for everyone. Personally, for a simple website my monthly hosting cost is £5 and since I manage the entire server, everything is backed up and secure - everyone is a winner. The developer may also register the domain name for you, but it's normal practice for the client to register the domain name as you will want ownership. But it's a simple process that a good developer should guide you through. I register all my domains through 1and1 as that's where my server lives and generally they offer a good service.
Just get the bare essentials
If you are selling a product or service on through your new website, and its just one or two things, you don't necessarily need a fully fledged checkout system. Services like Google Checkout or PayPal can be easily integrated in a "buy it now" type way, or cheaper still an email invoice system - where you invoice the customer via email. These systems can always be upgraded as your business starts to grow, when that happens, you'll have more funding behind you and it will be clear that you have a viable project so will be worth investing that little bit more.
Conclusion
It isn't fair or realistic to expect a designer to drop their hourly rate, and to be honest, anyone who does probably should be charging less to begin with. However, you can still get a well made website just by following the simple steps above. A developer can work his or her way around pretty much anything you throw at them (we are a resourceful bunch), but if you really want to keep the costs down then help them to help you :) A good website need not cost the Earth.