print from new 2nd PC on home wireless LAN?

[For the record, networking ain't my thing. Perhaps this is covered somewhere else, but I have no idea whether it involves hardware, software, networking, drivers, or what. Please accept my apologies and let me know if there is a more appropriate forum I should post to, or if the answer is already posted in detail somewhere else, even though I didn't recognize it.]

I have a home wireless network with wireless to the printer & wireless to the internet router (old house, easiest way to do). It's about 4 years old, so there is a linksys wireless-G 2.4 gHz involved. Printer is an HP Photosmart 7350.

Son's PC just got replaced. New PC had some difficulty even "seeing" the internet, but somehow he got it working himself when I took too long to address the issue. (Where there's a will, there's a way!) But we still can't get it to "see" the network printer. (I believe he used to be able to print to the network printer from his PC, but perhaps I'm assuming or imagining it.)

On my PC, it says the printer is set to "shared", but on his PC when we try to add a printer, it's asking for a path or a file/disk. I don't think I have a disk. There's something displayed on my PC about needing to have extra drivers to let others access the PC.

We're both running Windows XP, but his is quite a bit newer. I was going to download whatever other XP drivers I could find on the HP website, but it was cagey about the Photosmart 7350 & a particular version of XP (64?)--not sure if that's his version.

My long-winded question is (multi-part, of course):
--Should my son's PC "detect" the printer as is?
--How do I know whether it's a driver version?
--How do I know which driver to download?
--Where do I get the driver(s) if they're not on the HP website?
--Do I put it on his PC or mine?? (Sounds silly, but my PC made it sound like I needed to put it on my PC as opposed to the PC that will be sharing it)
--Are there other things I need to understand or do regarding our home network?

Bonus question:
I also have a new laptop that I had hoped to use for internet & printing from downstairs, but even with an antennae amplifier, it can't keep a steady connection. (Old house problems?) It too cannot "see" the network printer. (Makes it just a big, expensive "pad of paper", which is horribly disappointing.) Would a similar fix work for the laptop??

 

networking can be fairly easy however there is always that chance that something is not going to work , for instance your old house and the signal loss. I've also included a link to windows on setting up a home network.. home networks