I am trying to find a company that will place my web page on serach
engines.  At one time I used befirst.com but I can't find them.  Can
you give me a list of companies that offer the service of listing your
web site so that when searched it comes up first?

What you want is called a search engine optimizer or "SEO"

The one I use is http://www.spidersplat.com
but there are a zillion others.
This is probably a very complete list of them:
http://dmoz.org/Computers/Internet/Web_Design_and_Development/Promotion/Search_Engine_Optimization_Firms/

Your best bet is probably to buy some paid link space on a site like
Overture.com. http://www.content.overture.com/d/USm/adcenter/index.jhtml
Overture offers pay for placement bidding and then syndicates those
results back out of other sites.  It could be expensive though,
depending on the search terms you want to buy.  Try going with
something very specific at first and branching out from there.  If
your product is say, car seat covers, don't purchase a generic term
like 'cars' or you'll bust your budget with millions of impressions. 
The more targeted the words you purchase, the better your click
through rate (CTR) will be.

You can even purchase paid link space on google. They are not exactly
"true" search results, but are the next best thing.  They are also
syndicated out to many other sites. ://www.google.com/ads/

Befirst can be found at http://befirst.com

ldcdc-ga

Be wary of any service that guarantees a #1 ranking, and keep in mind
that every webmaster in the planet wants to be #1. The mostly likely
to get there are those with the best web sites, not the best search
engine optimization.

robertskeleton-ga, you're talking about the ideal search engine...
which unfortunately doesn't exist.  :-(

Just a thought...

ldcdc-ga