I need to but a modem/router adsl2+, WHICH?

Ok, I need to buy a new router for various reasons. First of all, my connection is completely "exploded", I hook to my ISP but I have 0.3mbit of download (and 0.5 of upload), while I usually have a 7/0.5 mbit (download/upload), so they asked me to test with a different router.
Second, I need a way to turn on my computer from remote, and by remote I mean through the internet, not through my LAN or wireless network (this is because sometimes I need to use it remotely through teamviewer).

From what I've read so far, I need Static ARP Table on my router (currently I have a LINKSYS WAG200G, which doesn't have it) because I must teach my router that should hook to my mac address. I also need a motherboard that support this: I currently have ASUS Rampage III Extreme, I don't know if it supports this, but I can see the motherboard leds (expecially networking leds) turned on even when PC is turned off, so I suppose that it supports it (I can still buy a network card if it's required, please let me know).

Now, I can spend up to 150€ for my router, and here you can find the features I'm looking for:
Static ARP Table to turn on PC through internet
Possibility to connect both through ethernet (possibly 4 cables at least) and through wireless (5 devices at least)
Port forwarding/routing/blocking capabilities
Wireless network should support 802.11b/g/n
Must be ADSL2+
Should be silent, I have alread a lot of noisy device in my room
DHCP Server capabilities (I use static IPs for cable connection and DHCP Server for wireless devices)

These are must have features.

What I would like to have:
My current router has an internal firewall, I don't know how it works this, (I study computers but definitely I'm not a network expert) but I would like to have something similar
Some QoS support? I actually need to install a netlimiter program to avoid my sister killing me while playing LoL just because she started downloading something, is this possible? My current router supports only QoS on ports, and the problem is that I can put only 3 customized ports, basically is useless. Are there anything better out?
Possibility to backup/restore configuration, will be really nice
Management through WLAN will be nice too

If you want suggest other features that I should look for, just post here.

Notice that I live in Italy (EU West), buying from amazon is a good option because I have Amazon Prime, anyway the important part is "I would like to receive it fast" if possible, I can still wait for it if I'm going to buy God Router from USA or something similar ;)

Thanks for any suggestion
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More about modem router adsl2 which
  1. Forgot two things (required):
    Good wireless signal (currently I reach everywhere in my house, except for the kitchen, it's ok in this way too but I want a similar signal)
    Should not crash for overheating or any other things: it must work.

    Not required:
    Replaceable antennas? (can you eventually point me to a powerful antenna?)
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