I've tested with most of these devices, and it works great! The main thing to remember is that all devices need to be updated to the same version of Minecraft PE.
Cable modem: Typical way of connecting to the internet is illustrated (but you can also use DSL, satellite internet, etc.). There is usually some kind of modem that acts as an interface. In certain cases, the wireless router and cable modem may be combined into one, but I don't like that option as much because the internet provider usually provides the cable modem and you don't have a choice as to what they give you.
Wireless router: Needed in order for more than one device in your home to share the same high speed internet connection AND to give your wireless handheld devices a way to get to the internet. You actually don't need the internet connected to play multiplayer Minecraft PE, but the wireless router will create a home network for you that your devices can all join... and thus be able to find and connect to each other. Pick a router up from Walmart or NewEgg.com.
NOTE: I had a lot of problems in the past with wireless routers. Finally, wireless routers are being made more reliable. If you stick to the NEW stuff, it should work well for you. Look for "Gigabit Internet" and "Wireless-N" standards. I currently have a TP-Link Archer C50 wireless router I am EXTREMELY happy with - it has been very reliable.
Windows 10 PC: You can now get the Windows 10 Edition of Minecraft which is fully compatible with Minecraft Pocket Edition! Yes, a Minecraft PE device can join a Windows 10 game or vice versa! Hardcore gamers HATE the Windows 10 edition because it has fewer features, but here are the benefits:
Mobile devices: Minecraft PE is generally available for all platforms! This includes the new Kindle Fire Kids. Note that if you purchase a license for a platform, you can generally use it on an unlimited number of devices for that platform (e.g., if you buy Minecraft PE for iOS, you can use it on as many iPhones, iPads, and iPods that you want), but you may have to buy it again for Android. But it's cheap ($7), and worth every penny!
I've experimented quite a bit with this. The short answer is: Older PCs are not fast enough to run Minecraft PE. I've tried several Android emulators. The really good ones are too slow and lock up the PC. PCs that are fast enough are usually running Windows 10 anyway, so you'd just use Windows 10 Edition. The best emulator optimized for performance is Blue Stacks. This works pretty good for apps such as YouTube Kids but still fails with the latest version of Minecraft PE.
UPDATE!!Blue Stacks has recently released "Blue Stacks 2". Unfortunately, they have disabled Blue Stacks 1, so you HAVE to use 2, and version 2 is much slower than 1. This is not a problem for most of their users, but IS a problem if you are trying to get Blue Stacks and Minecraft to work on an older PC. The new verdict is... you can't do it! Save up your money for a decent mobile device. Shop around. You should be able to get a Kindle Fire, for example, for less than $100. Then you can use the latest and greatest Minecraft with a touch interface rather than struggling against the odds. I will leave the last two paragraphs below for historical sake, but I recommend going another route!!
Old: You can get very old versions of Minecraft PE to work (e.g., 0.9.0 alpha). Note that multiplayer is NOT an option because the version will not match the version of other devices in your home, and the "infinite" world type will probably be disabled (because the older PC isn't powerful enough). Old versions of Minecraft PE are not available in Google Play, so you will need to download the *.apk file (Android package file) and install it. Note that this also means you can get it for free. Microsoft is probably tolerating this right now because the versions are so old and limited, and you probably already have at least one other device in your home with the latest Minecraft PE that you've already paid for.
To download 0.9.0 alpha, click here to get to the YouTube video (there may be similar videos also), and look at the DESCRIPTION for the video where you will find the download links. Assuming you've already installed Blue Stacks 1, just double-click on the *.apk file after you've download it. Easy. NOTE: If you ever decide to CHANGE the version of Minecraft PE in Blue Stacks 1, you need to un-install it first (manually) before attempting to use another *.apk file.
With some of the more recent updates of Minecraft PE, Microsoft has been pushing "Realms". We have been trying it since January (2017) and will probably continue using it past the free 30 day trial period.
Basically with Realms the setup is exactly as shown at the diagram at the top of this document EXCEPT that the world is hosted on a remote server (run by Microsoft / Mojang) instead of one of your family's devices. The main advantage is that the family member hosting your family's world doesn't have to have Minecraft PE running on that device any time any other family member wants to play. The server is always running, so family members can log in or out at any time. ALSO, you can play even when you are not at home, as long as your portable device has access to an internet connection. You can even invite friends to your world that might live at a different house!
We found it a little bit complicated to set up. First, every family member has to have a SEPARATE Microsoft account. Then when you start Minecraft PE on each device, you use that account. (If two people try to share an account, when the second person logs in the first person gets kicked out.) Second, even though family members can log in and out at any time, only one person HOSTS the world (sets it up, pays for it, etc.). The host needs to log in to the world from the "Worlds" tab; all other players log in from the "Friends" tab (assuming they have been invited by the person hosting).
Once it is all set up, it seems to work very well (assuming you have a fast, stable internet connection). We get kicked out occasionally, or have a crash, but not any more so than local playing, and we haven't lost any changes. You usually just log back in. Occasionally the server will be down for a while but it is usually back up in 10-20 minutes.
We like the fact that you get a free 30 day trial. This way you can make sure everything works reliably and well before actually paying. Also, $3.99/month is very reasonable for all the fun your family will have together. That gets you up to 3 people. We are GUESSING, but haven't been able to confirm, that you can have/invite as many family members and friends that you want, but only 3 can actually be logged in simultaneously. If you need more than 3 at the same time, it is $7.99/month for 10 people.
Q: Can you use seeds?
A: It doesn't appear so. If you don't like your world, just reset it OR use nether portals to go long distances to get to other biomes that you might want. If you have the Windows 10 edition, there's supposed to be a way to upload or download worlds, but we haven't tried that. We're just trying to keep it simple and have fun as a family.
Q: Can you do both Creative and Survival?
A: Yes, but not at the same time. You CAN switch modes (or keep switching modes). Basically you can do most anything you can do if you were hosting locally.
Q: What happens when Minecraft PE updates?
A: They actually have a good solution for that, though terribly documented. Basically the Realms version follows the version of the person HOSTING the world. So, if the person hosting just upgraded to Minecraft PE 1.0.3 and then tries to enter the world, the Realm self-updates to 1.0.3, and now everyone else who tries to join must have that version. (It looks like it is NOT forward nor backward compatible - everyone has to have the same version. BUT you can control when your family updates, if need be.) NOTE: Expect the usual round of bugs/quirks. We upgraded from 1.0.2 to 1.0.3 and a lot of our farm animals disappeared.