Which relays should I buy? Can I trust the ones from aliexpress? Should I buy a shield? Any advice would be helpful.
Search for "remote control power outlet" on ebay.
Arduino can replace the transmitter that comes with them.
What will be the load current, are you driving anything inductive?
Remember there is safety to consider.
cheapest way is to use a wall switch and just manually turn it on and off.
as for relays, cannot just buy anything. in the USA, the circuit is protected for 20 amps. you have to have a relay that can handle 20 amps.
anything else is potential fire risk and if you burn your house down, the insurance company has ground to not pay.
find a local electrician and ask them. their license is your guarantee of a legal installation.
How much current you want to switch is critical.
I have a card that can do 5A, you could wire the relays between the AC hot line and the hot of the outlets.
Here it is in shield format switching strings of LED lights.
The relays are rated for 5A, I made the traces as wide as I could top & bottom, they can also be reinforced with extra wire soldered between the relay pins and screw terminals if it turns out the traces need help.
Add an AC fuse to Crossroad's board, to limit the total load current.
For higher loads you can use ssrs however be mindfull of the total power drain 8x could require if all powered on at the same time and the arduinos limits..
Not the cheapest option https://www.itead.cc/sonoff-wifi-wireless-switch.html @ 5usd, but worth a mention due to the capacity ( to reflash with your own code all you need to is solder on a 5 pin header to gain access to the rx, tx, gnd, vcc, gpio0 and gpio2? iirc of the embedded esp8266 )
How far apart are these outlets? If they're in different rooms then look at Moteino or X10 wireless control.