I recently bought a Dell laptop that has B+G

yes you can work with it.

If you face problem in gettings signal strength then you need to change frequency channel in router.
for that access your router with following link
If it is not in netwrok then connect your router to computer with ethernet cable.
Then access thisd link http://192.168.1.1
or
http://192.168.0.1
type user name as "admin" and password as."admin" or blank or "password"

then if you cannot access it then you have to reset your router to factory defauls settings.
For reset you have to press RESET button for 10 seconds it is in back side of router .

then access with above link
then go to wi fi and change channel type to 4 or 6 or 11 try 1 by 1 then save settings in router then restart bot computer and router to then check signal strength set that channel which give you high signal.