I'm trying to figure out if I can buy just an airport extreme or if I need to buy a airport express base station as well? I just want to use it to replace my existing low quality router and use it for wi-fi access. Most likely I will not be using it for any other wireless purposes.
Also, how far is it's effective range? 20-30ft? More/Less?
Apple uses the term "base station" to describe their AirPort routers. You can use either term interchangably. Both models are, by default, wireless Internet routers and both will require an Internet Broadband modem for Internet access.
As far as range ... in an unobstructed area both have a useable range of around 150'.