If you have a PC running 24/7 the idea mentioned by CollinR is probably easiest. You shouldn't become a spam relay because you would NOT open port 25 inbound in your router.
A quick Google search turned up a few dozen free/opensource SMTP servers for Windows - or if you are running Windows Server it is built in. Of course Linux has it's share of them as well.
When looking at SMTP servers - try to find one that lets you use a smarthost. The idea here is that your SMTP server will forward all mail through your ISP's servers rather than trying to connect directly to the destination mail server. Many ISP's mail servers will not accept connections from "home grade" connections - there are a variety of issues to work around this but it is generally just easier to bounce through your ISP's servers.
A quick Google search turned up a few dozen free/opensource SMTP servers for Windows - or if you are running Windows Server it is built in. Of course Linux has it's share of them as well.
When looking at SMTP servers - try to find one that lets you use a smarthost. The idea here is that your SMTP server will forward all mail through your ISP's servers rather than trying to connect directly to the destination mail server. Many ISP's mail servers will not accept connections from "home grade" connections - there are a variety of issues to work around this but it is generally just easier to bounce through your ISP's servers.