Going from dialup to broadband - need help with modems

I have 3 computers connected by a hub - 2 are windows machines and 1 is running suse linux. The linux box acts as the main firewall and connects to the internet through dial-up, and the two windows machines can go online via the linux proxy.
I took a little while to set up right but seems to have worked well enough. But it seems dialup is now too slow, and system updates are taking literally hours to download. So if I have to transition to broadband can I replace the dialup modem with a broadband one and keep the system similar?
I do not need wireless equipment - the computers will not be moving, the network is fine and wireless stuff never seems to work in our house anyway - But most broadband stuff (I have seen) seems to be wireless?

Having no experience with broadband means I am uncertain with some of the terms... What is the difference between a 'modem router' and a 'router'?
I am thinking I need a modem router, but not a USB one? - Does anyone know of a good non-wireless broadband modem that will definitely work with Linux?

Quite a few questions, I know, but most info seems to be sketchy with the emphasis on 'Fastest download speeds' and 'Internet access from the bottom of your garden'??

Any help would be much appreciated
Thanks

I'm pretty useless at networking anything, but I find it helpful with any setup that's getting kind of complicated, is to sketch it out. If you don't understand if something you've sketched will work, or don't know what equipment you need, then you can ask specific questions (which are usually easier to answer)

Sorry I couldn't be of more help,
-Bernard.

- Thanks for the reply, I was beginning to think no-one would answer :???:

I have a few diagrams of my 'custom' network that make sense, but mainly I want to replace my dialup modem with a broadband one.

But I will have a rethink and re-phrase the question, maybe in the SuSE section

Anyway, thanks again for your post :)