If using a coax, do I need to balance the wire with the coax, otherwise I'll loose signal?
No. You're thinking about maximizing signal strength, but the real issue is always signal to noise ratio. Getting rid of the coax will indeed increase signal levels, but it will in most instances increase the noise even more, so it's a net loss.
There is no need to balance a coax-fed antenna as long as the coaxial shield is well grounded. You will lose signal due to the impedance mismatch between the wire and the coax, but this is generally not a major difficulty except possibly at a few "antiresonant" frequencies.
Antiresonance declines in importance (and frequency) as the antenna is lengthened. You can also use a matching transformer between the antenna and the coax to supress antiresonance.