Im starting a new project with friend and this prooject needs us to have out site accesible from an IP address and a domain name.

I know most hosts allow you to buy an IP, But will this mean our site is visible from http://123.123.123.123 and domain.com?-

Yes, if you buy a dedicated IP, then both the IP and the domain will bring you to the site.

Why do you need a dedicated IP? Remember, you can't get one without a good reason anymore.

Try DNS Exit. You can buy a domain name and point it to your IP address so it will be accessable by either one.

http://www.dnsexit.com/

You could also use No-IP.com for this...

http://www.no-ip.com/

Is someting like this also ok, http://123.123.123.123/~username ?
If you have hosting with cpanel or direct admin you can go to your site like this, dont know about other control panels.

That only works if you have a shared IP address and should only be used as a temp untill your domain propogates.

I contacted dreamhoost and they said if i purchase an IP my site will be visible from both IP and domain, so i think ill go with them.