First, understand that any idea of network classes lost its relevance sometime in the mid 1990's. Protocols where classes were significant have versions that accept subnet masks as additional parameters and do not care about what class an IP address is in.
There are three ranges of private IP addresses, and one for each class, but the class doesn't have any meaning anymore, unless you are using an ancient protocol that doesn't let you specify a subnet mask with IP addresses. What does have meaning is the subnet associated with each "class":
RFC1918 name IP address range subnet mask
24-bit block 10.0.0.0 - 10.255.255.255 /8 or 255.0.0.0
20-bit block 172.16.0.0 - 172.31.255.255 /12 or 255.240.0.0
16-bit block 192.168.0.0 - 192.168.255.255 /16 or 255.255.0.0
If your company is really distributing private addresses to customers (this is called Carrier Grade NAT), then you are stuck with what your ISP provides as far as the interface where your computer or network connects to the ISP.
Second, your router has two interfaces. One faces the IP and receives an IP from your ISP's DHCP server. The other is facing your network and completely up to you what you do with. Now, if you are going to reuse any addresses your ISP is using, then you will have to juggle some complex NAT rules. A consumer-level router may not support such complex NAT rules - a Linux PC with iptables can do it but it's difficult to set up.
So, it is possible, but usually a lot easier to just select a range your ISP is not using. It doesn't matter which one. 10.0.0.0/8 is typically what businesses choose by convention, but it is just a convention.
Now, with the right NAT setup, you could pick any IP range out of thin air and use it on your home network. However, if your configuration has an error, traffic destined for your home network may go to external hosts instead. The above "private" IP ranges are agreed to be "non-routable" - if they happen to make it to your ISP, your ISP is supposed to drop them. With carrier-grade NAT being an exception of course. So if you use a private IP range that your ISP is not using, it protects you from a consequence of accidental misconfiguration.
Best Answer
The IP address
0.0.0.0is used as a wildcard to bind to all addresses. The IP address255.255.255.255is used to indicate a local broadcast.Because this decision was part of the classful network design that predates CIDR, to reserve these specific IP addresses alone, special rules would have had to have been created for the /8's that contained them. Since some /8's were going to remain reserved anyway, it made sense to reserve these rather than creating additional rules so they could be used.