If you've got two pair, you can probably run 100BaseTx, even if the cable is not up to cat5 spec, especially if the runs are short and separated from other lines; Ethernet specs are for 100 meter distances most of which is in a tight conduit with other high frequency data transmissions. Old in-home phone wiring is likely not tightly packed or very long.
If you've got an old house with old telephone wiring, it's probably wired as a bus, if you want to re-use that for ethernet, you'll want to split it up so each phone jack gets wired as two ethernet jacks; one in each direction. If you're using ethernet in the room, you'll need a (small) switch, and you'll want to be careful to buy 10/100 switches if you've only got two pair as Ethernet autonegotiation can easily do the wrong thing and you don't want to pay for managed switches in each room. If there's no ethernet use in a room, still wire it up for two ports, but put a small patch cable between the two.
If you've got star topology phone wiring, there's a better chance of cat5 cabling and 4-pair and you can run gigE. GigE will sometimes run on cat3 for small distances too though. The only question is if the central location where the star wires meet is convenient for a switch. In a pinch, you can use a PoE powered switch and power it from one of the other ends of the star.
Of course, some houses are a mix of star and bus or generally some form of tree. Anywhere that there's a branch, you want to put one ethernet port for each direction. And hopefully all the branches are accessible.
There's really no need for DSL equipment in your own home, unless you've only got one pair wiring.