That's by definition of NAT works. If one defines a firewall to have blocked unsolicited requests, then all routers do this out of the box.
But the link you gave is not a bad deal and a known good product so why not?
Frankly I fear that your new router will suffer the same malady as your old setup. If the old router works with one machine but not another it's never been a router failure.
I've been using a router for a while, but I lost the disc to it. The firmware is still available for it online. Well, the new computer doesn't seem to pick up the Internet connection thru the router and I've tried many things to make it work. No success. So, I decided to have the router connect directly back to the previous computer and use the 2nd port on the router for this new computer. Well... The previous computer isn't detecting the Internet connection anymore. I dunno why.
I'm going to buy another router, so I can get a disc.
This is same or similar to the one I have. Mine model number for the router is WRT54GS.
I would like a router that offers firewall and security protection, etc. I uses the AOL Security Suite, which includes a firewall from McAfee.