Having trouble with multiple router setup.

I have a LAN connecting 4 Windows PCs and accessing the internet through a
router. The setup is this:

The cable modem directly connects to the first router and gives it a dynamic
IP.

First router has a LAN IP of 192.168.0.1.
It runs as a DHCP Server.
It has Internet Port Subnet Mask of 255.255.248.0
It has LAN Port Subnet Mask of 255.255.255.0
It connects to 2 devices: 1 computer and a second router, both of which
receive an IP in the range 192.168.0.2 - 192.168.0.254

So the second router gets a WAN IP of 192.168.0.XXX
and has a LAN IP of 192.168.1.1
It has a WAN IP Subnet Mask of 255.255.255.0
It has a LAN IP Subnet Mask of 255.255.255.0
It has a default gateway of 192.168.0.1 (the first router)
The other 3 computers connect to this router, and get IPs in the range
192.168.1.100 - 192.168.1.254

Here're my problems:

1. On the Windows Network, the computer linked to the first router cannot
see any of the computers linked to the secound router.

2. The 3 computers linked to the second router cannot keep a stable internet
connection, and I don't think it's because of the dynamic IP assignment
(they disconnect much more often than dynamic IP changes).

One router is an old Linksys. The other is a new Netgear. Both are 4-port
with Wireless 802.11 (b and g). Using the Netgear as the first router (i.e.
the one directly connected to the cable modem) seems to make things worse.
That is the setup I described above.

Should the two routers have different subnet masks? Any suggestions or
related networking info would be appreciated.