I am finally going to put up a VHF antenna for 2 meter and another antenna
for 70 cm.

What is type of coax should I use? Rg213? Or will RG213 be too lossy?

It depends on what you wan to do . As mentioned use the lowest loss you can
afford. The 5/8 inch hard-line is great but not many will want to pay the $
5 per foot and about $ 70 per connector and put up with the stuff not being
easy to bend.

Look at the LMR 400 or Belden makes some that is hard to find I think is
called 9914. It has almost the same low loss as the 9913 but uses a solid
dielectric instead of the hollow type of the 9913. If you are only using 30
or 40 feet and mostly the FM repeaters, the RG8x type is ok. As someone
mentioned the RG 6 type sold for cable TV is fine for a run of 50 feet or
so. The on;y problem is the connectors. IT is 70 ohm coax but for most
simple systems it will not mater.

I have used most all of the above but the hard-line at home and it all
depends on what I was doing. I only want a few local repeaters for a rig in
the house so a homemade dipole (vertical) is up about 25 feet on the tower.
It has about 40 feet of rg59 and then about 30 feet of rg58 going to it.
Not the best but it works fine for what I am doing. I also have a 2 meter
ssb rig in the shack that is fed with the 9913 and it seems to work ok for
it. Using a dual band antenna to a scanner that is programmed with 2 meter
and 440 repeaters and feeding it with about 100 feet of rg8x. The 2 meter
part works great but not so good on the 440 band.
The satellite antennas are feed with the 9913 and sofar I have been able to
keep the water out of the coax.