GNSS antenna properties
I think one of the most suitable choice would be a telescopic antenna since the market offers lots of telescopic antennas.

I don't think it works like that. There's a lot of cheap sand on the market. If you want to bake a cake, flour and sugar would still be a better choice...
Also, telescope antennas are extendable, and monopoles, and thus not multi-band matched to 50Ω!

HackRF One can easily acquire the signals if a suitable antenna is selected to its input port.

Nope. When you look at how GPS receivers work, you'll see that for noise figure reasons, there's a low-noise amplifier very close, normally even integrated with the antenna. This is necessary because the power density of GNSS signals when they reach your antenna is so very low that they'll just disappear into receiver noise in your HackRF.
So, you need an active antenna. And to supply that with power, you need a bias-T, too.
So, buy a commercially available GPS/GNSS patch antenna and a bias tee.

one thing that should be accounted which is antenna's gain

nah, not really unless you know how the antenna is going to stay in a fixed orientation. If it does, 3 dB is the gain you want - that's the gain you get when you don't observe the half of space where the earth is. You need to get multiple satellites for any GNSS to work, so the observed part of the sky mustn't be too narrow.
Again, commercially available GPS antennas.