Help my understand subnetting?

Lets use the subnet 192.168.1.0/24 as an example. (The /24 means netmask 255.255.255.0)

Yes, you have anything from 192.168.1.1 - 192.168.1.254 available to use as host IPs. You can choose any address you want within this range, and assign it however you wish to any devices on this subnet. Just make sure you don't assign the same address to two different network interfaces, or (obviously) you'll have headaches.

You're also more-or-less correct that if you're interested in setting up a simple subnet containing less than 254 hosts then a netmask of 255.255.255.0 is sufficient. If you wanted a larger subnet, then you could instead use a netmask of 255.255.0.0, and then have 192.168.0.0 - 192.168.255.255 available to you (see below for a list of private address ranges.) There are other reasons you might want to use a different addressing scheme, but for a small set up what you're describing is sufficient.

Using a netmask of 255.255.255.0, you wouldn't want to assign an address of 15.87.156.x, because that network range is not considered a "private" range. In other words, 15.87.156.x is part of some publicly assigned block of addresses - assigned for use by Hewlett Packard if I'm not mistaken. Actually, because it's a publicly assigned block, it wouldn't really matter what netmask you tried to use.

Address spaces assigned for private use include:

10.0.0/8 (255.0.0.0)

172.16.0.0/12 (255.240.0.0)

192.168.0.0/16 (255.255.0.0)

Note that with the deprecation of classful addressing and emergence of CIDR, it's now become commonplace to further sub-divide the above private addresses.

Hope this helps at least a bit;

Wire

Indeed, using different masks is driven by the number of hosts needed in the subnet.

On a LAN, you can use any address from these ranges:

10.0.0.0 - 10.255.255.255

172.16.0.0 - 172.31.255.255

192.168.0.0 - 192.168.255.255

all other ranges are subject to be taken by someone else on the Internet, and therefore are not recommended for local use.