Canada, want a good PCIe wireless adapter

My budget is about $50. My IPS provides me with a 50MB/s signal, and I want to be able to reach the full speed. My PC is in my room, the router is in the living room, which is about 7 or 8 meters away. There's a wall in between. Is it possible ? If it is, recommend me a good wireless adapter that can do it for my budget.
 
First off, your ISP probably provides you with a 50 mbps connection, which is equivalent to 6.25MB/s. Just to clear that up. That being said, chances are that you won't reach your full speed. You need to tell us what type of wifi your router supports before we can help you, it will most likely be 802.11a/b/g/n. N is the only type that would give you a chance of downloading near the speeds you have. But at a range of 8 meters, a wall, and additional interference, you'd probably be lucky to see 4MB/s download. You'll more likely see around 2-3 MB/s if you want the full speed, your best bet is wireless.
 
Yeah, sorry, 50 mbps. Right now, I'm connected with a cable, but it can't just go straight, so it's actually a very long cable, and it only gives me 10 mbps. Would I even see a difference by going with some good wireless adapter ?
My router is the Bell Sagemcom f@st 2864. I don't really know what specifications are important, here is the full list :

Spec:

• Network :
- Multimode VDSL2/ADSL 2+/GigE
- VDSL 2 : G 993.2
- ADSL 2+ : ANSI T1 413
ITU G.992.1 (G.dmt)
ITU 993.3, G.992.5
Annex A or B (option)
- Gigabit Ethernet
• User :
- 4 Eth 10/100/1000 Base-T
- Up to 3 USB 2.0 host for Accessories
- 802.11 b / g / n (draft2.0), WiFi access point in 2,4 GHz
WIRELESS SECURITY
• WPA/ WEP with 64 or 128 bits key
• MAC Address Access List
• Easy Pairing (WPS)
NETWORK
• VDSL2 and GigE
- General : up to 8 VLAN
- Encapsulations : IP/Eth
RFC 2516 (PPPoE)
• ADSL 2+ :
- ATM AAL-5
- UBR,CBR, VBRrt, VBRnrt
- Up to 16 Vcc
- OAM cells
- Encapsulations : IP/ATM
Eth/ATM
PPPoA, PPPoE
PPP FUNCTIONS
• PAP/CHAP
• Multi PPPoE sessions
• PPPoE client termination
• PPPoE session pass-through
IP FUNCTIONS
• General :
- NAT/PAT
- DHCP client and server
- DNS relay
• Routing :
- Static/dynamic routing
• IGMP Proxy/snooping
• Firewall :
- Address, port and protocol filtering
- State full Packets Inspection
• Quality of service : DiffServ
MANAGEMENT
• Firmware upgrade by FTP
• Auto provisioning by ftp
• Configuration : http, Telnet
• http Quick configuration
• TR-069
ELECTRICAL SAFETY
• Compliant with EN 60 950, EN 41003
ENVIRONMENT
• Operating temperature : 5°C to 45 °C
• EMC : 89/336EEC
EN 55022 Class B
EN 55024
PHYSICAL FEATURES
• External Power supply
 
Are you running a cable directly from the router? More importantly, what type of cable is it. See if you can find the Category rating written on it, should say something like CAT 2, CAT3, CAT4 etc. Where did you get the cable and how long is it? While I think you could get better connection than what you're currently getting from the cable, You won't be able to get the full connection.
 
Single cables are always the better route, there is no chance that you'll have something like a coupler problem, and if the cable is bad, you'll know. As far as wired vs. wireless, it will be much cheaper and you will get better results with a wired connection.
 
Then I'm just going to go with cables. I'll need two, as I also got another PC to connect with it. I want it to be as cheap as possible, and get something that will be long enough. Lets say 25m, if it is possible, just to make sure. Do you have any to propose me ?
 
These are 100ft cables, so about 30m cables, but for the price it it's hard to beat. You'll probably be fine with unshielded cables (UTP) and if that's what you want this is 100ft for 11.17 USD:
http://www.monoprice.com/products/product.asp?c_id=102&cp_id=10208&cs_id=1020814&p_id=2164&seq=1&format=2

If you want to be extra safe, you can get shielded cables (STP) for about 6 dollars more:
http://www.monoprice.com/products/product.asp?c_id=102&cp_id=10208&cs_id=1020816&p_id=6992&seq=1&format=2

Up to you, the UTP cables come in the entire rainbow, if you're interested in that stuff, but STP ensures no interference from whatever may generate EMI (see: any cable that runs electricity).