Yes the RG-213 should do fine..
For the record though ( since you asked)
RG8..RG-213 and LMR-400 are Not the best out there..
of those 3 you spoke of...LMR-400 is the best..
The Fact that you are using it for 11 meters and likely require no more then 100 feet ( and do not Persay want to spend for the Truly Best) then i would say use no less then RG-213..But given that LMR-400 is cheep anyways..then i would go with the LMR-400 or the Beldon 9913 flex..
There are many coax caculators that can show you the loss you would sustain using whatever coax feedline you decide to use..
Many here Blast me for being too extreme and or willing to spend too much money..
Earlier on in the tread one stated LMR-400 does not bend easily ( so he suggested Bendon 9913 Flex)..
Well on HF ( Mostly on 11 meters ) i use True Hardline
Andrews Heliax LDF5-50a ( which is 7/8 inches thick )
This because i use a 140 ft to my Interceptor I-10K..So i encur very little loss and i can be fairly sure i will Not need to replace it for at least 10 years ( its warrantied life span )..
Also i am far less likely to have issues with neighbors due to RF leakage..
However it also seems to enable my radio to "Hear" better without having to put an antenna mounted PreAmp on..
For VHF and UHF i instead use Andrews Heliax LDF7-50a (1 & 5/8 inch coax feedline )..
So..
Be careful when you ask...
What the BEST coax is..
What i use is not even the Best..But is what typically cell phone carriers use for 900 to 1900 mhz (with LDF5-50a ) So i suppose it is good enough for me on HF..
Good luck on your new antenna set up..
The Better you set it up now..
The easier it will be to keep working good and the less issues that will pop up down the road..
Actually you are not using hardline, you are using heliax. Hardline is actually rigid copper pipe that is in no way flexible at all.Probably 98% of the people call heliax cable hardline so don't feel bad. real hardline looks like this.
I have installed both and believe me heliax is far easier.