Correct me if I'm wrong but 56K is analog in the voice frequency (~20 KHz). Its response time was slow because of that. DSL runs in the 100s of KHz and is a digital signal versus analog.
QAM and its variants and lattice compression.
All DSL and Cable have done is increase the number of signals through better and more complex compression that we were unable to cost effectively perform years ago by moving up to 64, 128, and 256 bit QAM and using lattice compression to bit check the data with minimal overhead in processing to reduce latency.
This is also why some media types are slower, they cannot be compressed or the compression applied to them results in unacceptable artifact.
Plus the advances in termination and load calibrations and much else has been huge in cleanliness of the signal, thus costing fewer parity check bits and larger QAM "words".
OP
You are looking for two separate things, first is your peak theoretical bandwidth. As in , I purchase a slice of a pie that can reach a theoretical peak of lets say 100MBps. However every residential connection in the US is oversold, ISP's know users will rarely use all the bandwidth they buy all the time, so if we follow the 70% bend of the knee rule we can oversell a 1Gb connection by 30% with no real noticeable degradation of service, most seem to follow a 50% or lower bend of the knee rule though.
So lets say you are in a perfect world and your connection is not being throttled by your ISP or oversold. We then find the next weakest link in the chain, usually the router you use, or modem and router assembly. Since they are trying to get by with good service but as cheaply as possible the amount of processing the modem can do is generally limited, and once a connection limit(not physical, but port/IP/service connection aggregation) is reached delay may be added as the packet waits for the CPU to route the packet to the originating client/server.
The hardware limitation of bandwidth in routers is known as backplane bandwidth.
For example a 8 port Gb switch really only needs 4Gb of backplane bandwidth to service all 8 ports at full speed, but depending on MTU this may require more storage and processing than is cost effective in the $29 piece of hardware, so you may only get 2Gb, or 1Gb, meaning that when two other computers are transferring data at high rate your internet may slow down in latency and throughput.
I reviewed a set of power-line Ethernet adapters and they added 3ms to my latency, and were only capable of 30Mbps despite having a higher rating.
If you want to know your absolute "ping" or turnaround times start with your internal network, then start moving out to the local ISP subnet, then to usually their primary node, and then to a webserver. Average a few runs with each and subtract the numbers from your network to the ISP's last node to determine where and if a problem is.
So for example.
ping 192.168.0.1 (local router interface) 1ms
ping 111.10.10.10 (your modem WAN IP) 3ms
ping 111.0.0.1 (local subnet gateway for ISP) 7ms
ping 123.456.789.12 (ISP primary gateway) 13ms
ping
www.google.com 46ms
Subtract the first 4 numbers, and do this test while your network is in use, and also off primary hours for the ISP and during.