the modem you would normally plug the wireless router into is I think a DHCP server or is simply a passive device.
you should use an AP instead on a business network. whether or not you need a long range AP or not is up to you and the FCC. a long range device could also mean a security concern if someone outside the building decides to tap in.
there are also mesh networks as a possibility. see the cyberguys.com catalog.
IT/IS should know about any devices like this you intend to add to the network,because they manage the network I would assume, and oftentimes rogue APs and wifi are a problem,maybe especially in the case when it's a managed network.
- if there are any other APs in the area, you want to make sure you are not on the same channel. this will be evidenced by "dropped wifi" and you will have to reconnect all devices once you have established the new channel.
- you should ALWAYS secure your wifi with a unique SSID, passkey, and at least WPA2-psk/personal AES encryption. if you don't have this, mixed encryption is also workable. TKIP and WEP have been cracked. mixed defaults to AES but can go down to WEP if the device won't connect with AES.
an AP is an Access Point. it is basically wifi without the router (does have a web server for configuration and some features though).
those IP's are probably safe because everybody uses something like those, but I wouldn't go around posting the internal IP's of your company equipment on the internet. it's a way to get hacked. be hypothetical.
so if you can, edit them out.
disable NAT and nobody in the LAN side of the router will have access - people will be upset.
ahh - you must be the IT guy.
the router can use a DHCP server on the internet side, or it can use a static IP.
you can have static IP's outside the DHCP server range on the WLAN(wifi)/LAN side. this is for devices like APs and network laser printers or HP Officejet 8600 (5-users max) or wireless ethernet bridges (cool devices- makes networklasers wireless - sometimes called wireless ethernet gaming adapters - I like the old name better).
having a router behind a router is not a good idea unless you MAYBE turn off the SPI firewall and turn it basically into an AP. you might still need NAT though,but I seriously doubt NAT on NAT would work.you would plug the internet side into the switch side of the main router. that might work - maybe.
setting everyone up with a static IP would be painful. your DNS servers would all need to be updated periodically if the ISP's DNS servers change (and they usually do, but slowly).
leave the dhcp server on the router on. if the router was set up for DHCP on the internet side, leave that alone. print out those settings and file them in case of a need for a reset!
I don't know if you specifically requested a static IP from your ISP or DHCP for the internet side. you might have to contact them to find out about your account if you don't know. whoever pays the bills would need to be handy. the ip address from a remote computer doesn't matter - all you need to know is that it's getting an IP address from the DHCP server in the router.
read the router manual. it's probably on a cd or on the mfr's web site.
I was thinking that the wireless router should really be the replacement router for the network (might be better if it's stable), but I don't know what kind of router you have now, maybe it's better and you just need an AP).