As several others have said you are probably going to be better off using a Free Web Hosting provider such as X10Hosting or 000Webhost and there hundreds of others out there. However they do have rules about what you can and cannot put in your website, basically anything nude, naughty or just illegal and the will shut the site down.
Many ISPs do have a clause buried in the T&C's saying that 'Thou Shalt Not Run a Server' but provided you are not shifiting large amounts of data on a regular basis like movie files then you should slip quietly under the bandwidth throttling radar.
The old iMac G3 is ideal for home sever use because they do not have any noisy cooling fans and can be picked up for almost nothing. (I actually gave my last three away to Freecycle) Elderly laptops or newer ones with broken screens also make for good home servers and I'm presently running a seven year old Toshiba Lifebook with a 3G dongle to keep one small experimental site up.
Of course anything will do at a pinch right down to first generation stuff like PentiumIII and Socket7 chassis desktops when Win98, 64Mb of Ram and a 5 gigabyte hard drive was considered awesome. Unless the site needs to do a lot of number crunching or database manipulation then you don't need a lot of hardware resources.
BTW did you know Android phones can run as an HTML only webserver?