Cat3 SHOULD work for MOST applications. Cat5 & Cat5e is what is currently available. If this a new install, I would go with 5e or install EMT/NMT for an easier upgrade path. If this is an existing installation, AND the wiring is in good shape AND the customer is only doing basic Ethernet use, Cat 3 will function.
I'm not sure how much future proofing you should be doing, because the future might be Wireless and all of the installed cable will be not used. If you are going to install network cabling, I would think that a power receptacle should be in the next stud bay over.
I would not install CAT-3 for anything but POTS phones. The average homeowner LAN is pushing the original (published) CAT-5 limits at 100mz and if they buy a gigabyte LAN they have exceeded it. It might work but it is not supported.
The cat(egory) refers to the data speed it can handle. Cat 3 is overkill for phone at 16mz but if you have 2 lines you still need twisted pair so that is about as cheap as you can go. Cat 5 and cat 5e are for high speed data but that is becoming very common in houses so it is the defacto wire people install for everything. With the right terminations you can carry video, audio or just about any other kind of "data". Unless you do enough low voltage to carry a couple different spools of wire I think I agree, just use cat 5e for all your phone and data wiring.
I still don't think it is right for doorbells, garage door openers and thermostat wire (too small) but I see it.
VoIP to what/where? If the line needs to be used to support a fast Ethernet connection back to a central PBX or router, then yes, CAT-x would be needed. If the line is still just providing the DSL connection for the VoIP interface at that point, then no.
I think the point is that Cat 5 wire is not that more expensive than bell wire. You money is in labor, particularly after the wall is closed up. Why wouldn't the customer want the best wire they can get?
I install Cat5e at a minimum - even if its only telephone. All too often the occupants want to redecorate, re-organize, or add another computer somewhere else in a few weeks or months. Then the couple runs you put in the first time can be re-used for 100Mbit ethernet.
I try to push for a central 'media panel' if at all possible. Makes subsequent work easier.