mouse or mouse adapter question

I was wondering if anyone has used a mouse with the ps2 and if they'd be able toanswer for me the following:

1) Is there a mouse that is compatible with both ps2 and ps1 games?

2) If I use a mouse adapter compatible with the ps2, will it only work for the ps2 games? (I have come across one adapter that has a playstation controller port, but I'm not sure if the game will recognize it.)

I'm basically trying to decide between a mouse or an adapter that can be used with the ps2 but works for ps1 games. I am not paying the ridiculous 40.00 for the sony mouse so I was hoping an either an adapter or another mouse would work. I was looking at an adapter but I'm not sure if the game would recognize my pc mouse through the adapter. Here is one that I came across: http://www.amazon.com/Ps2-Keyboard-Mouse-Adapter-Game/dp/B000HIELHS/ref=pd_rhf_p_2

If anyone could let me know if something like this would work I would really appreciate it. Thanks.