This is a two-part question/answer.
...I read somewhere that it [half stitch] kind of distort the fabric in one direction, is
Well, I can only tell you what I know from my experience. Hopefully, it will be enough information.
First of all, I am stitching this in half stitch. I am not doing a tent/continental or basketweave stitch. It wasn't until the last couple of years, that half cross stitch has been
lumped in as a "tent" stitch. Tent stitching used to refer strictly to
needlepoint stitches. In my opinion, that should still be the case. Here's an illustration of the differences:
The stitches in black are half stitches; the red is basketweave; the blue is tent or continental. I am using the first (black) stitch.
Secondly, how you hold your fabric when you stitch can make a difference. I use scroll frames. The frames that I have are excellent! I got mine from Artisan Design. The fabric is held very taut and doesn't shift. If you were stitching in hand, I could see how you would have to be extremely careful with your tension to prevent distortion.
I have not seen any distortion in my stitching while using half stitches with my fabric in a scroll frame.
Cinzia also asked,
I was going to use an evenweave other than Aida, any
That depends on what you are comfortable with stitching on. Personally, I have great vision (thanks to lasik) so I am comfortable stitching on any count.
If you have primarily stitched on Aida in the past, I would suggest a gradual change. Maybe Hardanger fabric which is 22 count. If you want to make the "big leap", you could stitch on 28 count Lugana or Jobelan evenweave. Once I'd switched to evenweaves other than Aida, I was hooked! I only use Aida on the rare occasions where I purchase a kit that includes it. The kits that I tend to purchase are ornaments, so I don't use Aida for anything but smalls.
Only if you want a real challenge would I suggest trying linen. While you can get linen in 28 or 32 count, it is not an evenweave! Linen has slubs (variations) in thickness of the individual threads used in the weaving. This can cause the stitch count to vary slightly across the fabric in either or both directions.
Currently, I have two projects that I'm doing on linen. The PTP Floral Arrangement over 1 on 40 count and the Sistine Chapel over 1 on 34 count. There haven't been any issues with using linen for either project.
I hope this helps!