Link Aggregation between managed switch, unmanaged switch, and modem/router

I am trying to learn more about computing and networking for my own projects, while not interfering with my housemate's access to the internet ... I have:

• T2600G-28mps tplink managed switch
• TL-SG1024 unmanaged switch
• ArcherVR1600 modem
• TS-877 QNAP NAS
• Rack server ( donated by some friends who run a datacentre )

What I want to do is set up:

• Link aggregation for all 4 ports of the modem/router to the managed switch, so that all computers on the network get maximum bandwidth to the internet
• Any apporpriate VLANs to deal with network segements
• free communication between all VLANs, so that I can easily manage computers and send/share files between them
• additional subnets for playing with virtual machines for experimentation, learning, and development

But it seems that either I am suffering a lot of knowledge gaps and don't understand what I should be searching for, or perhaps I am getting something else wrong, I have tried many things, but I can't get it to work.

So, just to start at the beginning:

• The modem/router by default sets itself to 192.168.1.1, with all 4 ports and the wifi in VLAN1
• The managed switch by default has 192.168.0.1 as its management interface for its VLAN1
• If I use the CLI to reset the router ( from my last failed attempt )
• If I then set up a Link Aggregation Group in the managed switch of 4 tagged ports to connect to all 4 ports on the modem/router
• If I create a new switch VLAN to encompass these 4 tagged ports in LAG1 plus another 4 untagged ports to the unmanaged switch, plus additional ports directly to end devices, all ( minus the LAG & ports to the unamanaged switch) marked as edge ports
• IS THERE ANYTHING AT THIS POINT THAT I HAVE DONE INCORRECTLY?
• IS THERE ANYTHING AT THIS POINT I HAVE MISSED?

I guess this doesn't solve all my problems, but at least it would get me started. I thought this was all I would need to do, but clearly I am wrong, as it didn't work, and I tried many things, read lots of articles and help files, but nothing quite explained what I was missing or doing wrong.

I believe you misunderstand a few things - chief of which is that on a consumer router you can't typically plug multiple network connections between the router and the a managed switch to aggregate them (and even if you could, this it won't increase your performance because the modem/router can't push more then a gigabit of traffic)

I could be misunderstanding your post but it also does not seem to me that you don't correctly understand tagged vs untagged ports, and indeed its unclear to me why you are using VLAN's here (it appears you are only using 1 vlan - realistically (and making the very big and likely incorrect asumption the router supports it) you would want to set up 2 vlans on the router, with 2 networks and 2 gateways to keep you and you housemates traffic separate.

Realistically, you might want want to rething the whole way you have set this up. The simplest way, depending on what exactly you mean by "not interfering with my housemate's access to the internet" would be to have is Internet connect directly to the Archer 1600 router, and you get yourself another (ethernet - ideally dd-wrt capable) router and connect the wan of the new router to a lan port on the main router, and hang all your equipment off the LAN port of your router. You will need to change the LAN network range for your router - you might want to use 10.0.0.0/24 initially.