BT vs VM doesn't really make much difference. Only real difference is that BT deliver broadband using DSL over the phone wires so you would be likely to want a DSL filter where the phone line enters your distribution system to split the phone from the broadband. VM deliver broadband over the cable TV coax so broadband stuff is total seperate from phone stuff.
PBX is a term for "private branch exchange". Basically an internal phone exchange with features like internal calls, transferring calls to other extensions, ringing different phones for different lines and/or different times of day (so you might have a "day mode" where incoming calls go to a secratary and a night mode where incoming calls ring all phones) and so-on. It would be unusual to have one in a home but the norm in all but the smallest buisness premisis.
PBX's come in many types, the connection to the phone network can be through conventional analogue phone lines, ISDN lines, or VOIP. The connection to the individual phones can also be analogue, propietary digital, ISDN (though this is unusual), or VOIP. The system can be implemented in dedicated hardware or in software on a computer (which may be fitted with special interface cards or may be pure VOIP).
If you just connect multiple ordinary phones directly to the same phone line then you will have no ability to call internally between them. Also if you put too many phones on a line there can be problems with insufficient ringer current to make them all ring properly. Officially you aren't supposed to exceed a REN of 4 and most phones have a declared REN of 1 so that means a max of 4 phones, AIUI you can usually get away with a bit more but not all that much.
You can also use a VOIP desk phone directly with a VOIP provider. This can be a cheap option if you want a second phone with it's own number that is independent of your main phone line. VOIP is less reliable than a second traditional phone line or an ISDN setup but it's much cheaper and may be a good compromise if you need a second independent phone for a small buisness.
I guess the deeper question is why do you want so many phone points? Is it just because you are unsure which rooms you will have the phones in? Is it because for some reason you want a large number of wired phones? (don't trust cordless phones? have known issues with radio propagation in the house?) plan to run a buisness from the house?
Sets of cordless phones usually offer some level of internal communications features, so they actually provide more functionality than multiple corded phones on the same line while being much cheaper and easier to set up than a PBX system (which does offer more functionality than a set of cordless phones but it's functionality you would probablly only care about if running a buisness)
If you are unsure my advice would be to install CAT5e/6 cabling back to a central point terminating on a patch panel. Then you can hook things up as needed to either put all phones on the same line, split the phones across multiple external lines, install a PBX (of whichever type), patch the port as data and plug in a VOIP phone (or any other device that needs internet), whichever suits the circumstances at the time. You will probablly want to put in cat5e stuff for data anyway so this makes the phone wiring "more of the same".
