Okay, so a few things.

1.) Your internet speeds are only as fast as your ISP provides. This means that if you get 100Mbps download and 50Mbps upload from your provider, Cat6 cables that can do 10Gb are not going to benefit you anymore than Cat5a cables that can do 1Gb. This is especially true if the modem/router your provider has given you doesn't even have ports that support that speed. Most now days will have 1Gb ports, but unless you're an extreme enthusiast, you're not seeing 10Gb without SFP+, which I would bet almost everything you don't have.

2.) New cables are always a great purchase, especially if your's are real old. Cables can break down over time, and while unlikely, can hinder performance. The important thing is really what the cable is made out of. Do some research about shielding inside of Ethernet cables. Shielded Ethernet cables reduce noise, which could help with performance, but it certainly isn't going to give you any more speed than what you should be expecting.

3.) A VPN can theoretically give you better peering options and routing, if your ISP's suck. A lot of people do this for streaming services such as YouTube or Twitch.

Edit:

I forgot to mention that although having higher speed rated cables won't improve your Internet speed, they certainly can improve local network speed. Devices connected via your modem/router or a switch if you want to get fancy will share data at the maximum speed supported by the ports on your device. In my case, devices connected in my house all go through my 1Gb port Cisco switch, so streaming movies and music from one to the other is quick.

Thanks for your help. How can you find out what your provider allows?

(also i wish you didn't edit your post I understood what you were saying, oh well)

You would just have to check with whoever pays the bill for it, they would likely know. If you pay, then check with your ISP. They can tell you over the phone or probably online.

Also I edited it because while it was true at one time that providers used cache servers a lot, they don't really now'a days, so the example was quite outdated, and hard to follow for people who don't really know a lot about networking or computers in general.

Edit: Remember your speeds almost always up to the advertised amount. They aren't guaranteed.

Understandable, last question

How much does a SPF+ cost? (or a good one at least) I really am considering to upgrade the ethernet capabilities now that I moved the router into a position where we can use it

ty again for your knowlegde of 1970's cables

SFP+ probably isn't what you're thinking it is.

With SFP+, you're capable of pushing 10Gb between devices. Locally. It's expensive (compared to Cat5a 1Gb), and they require special connectors and cables you'd have to buy online and then install. Then in order to really be effective you need a switch that would support it. Those aren't cheap exactly either, and then not only all of that, but every device you want connected to 10Gb has to be able to reach the said network switch.

To put it plainly, there is a lot of money (compared to not doing it), and planning that has to go into having an enthusiast networking setup. You're much better off grabbing a much cheaper 1Gb managed network switch off of Amazon, and connecting everything to that. Your modem/router would plug into the switch, and the switch would then distribute any actual Internet connectivity through the port you have the modem plugged into.

Just lookup SFP on Google Images if you don't believe me.

1. Are you talking about cables, routers, switches or NICs?
Your network can only be as fast as its slowest part.
Cat6 cables cost a couple of dollars for 10m.
10G switches start at 300$. You'd need at least one. Routers are much more expensive.
You'll also need 1 10G for each device you want to connect to the network, that's at least 200$ each.

2. No. Unless you want to do rendering live to a fileserver at >100MB/s I don't really see a use case.

3. That's only the network inside your own house. That can be as fast as you want, to connect to the internet you need to go through your ISPs cables/network.
Those are most likely not even capable of 1 Gigabit.
If they are then you still have to pay for it. Those cables didn't suddenly appear over night and they are not connected to the internet via thin air. That all costs money and ISPs want to turn a profit.

So it's simple. Are you paying for Gigabit internet? If not then your existing home network is guaranteed to be faster at 1 Gigabit (= 1000 MBit). Look it up if you don't know, but you're probably paying for something between 1 and 200 MBit. Run a speedtest (http://speedof.me/) and check if you're reaching that "up to" number. If you do then that's as good as it gets.

#2/#6
SFP+ with twinaxial copper is garbage, specced to 10m for 10G. Standard Cat6 can do 55m, Cat6a 100m.
SFP+ optical is specced for 10km 10G and that is much overkill and so ridiculously expensive that I've never seen that being suggested for a home network.

But he could shave NANOSECONDS off of his ping guys...

Seriously though just get equipment that supports 1Gb Ethernet, their's basically no need to spend the extra dough for 10Gb ports, NICs, etc for 99.9% of SOHO (Small Office/Home Office) networks.

I mean yeah. Nothing changes, like I said, stick to consumer friendly and probably more than enough 1Gb. Not arguing for people to buy SFP compatible switches, then the modules, then the cables, and then the NICs.. It's just as of right now, it's the cheapest way to pull off 10Gb in a home network.