Running the elements through a metal (conductive) boom requires you to adjust the element length to correct for changes caused by the boom. Some commercial and plans-on-line designs mount elements on stand-offs so the boom is not in the plane of the elements. Easier than applying correction factors. DK7ZB has a wealth of info and designs on his pages. There may be some examples of this for switchable Horiz/vert polarity or circ. polarization antennas. M2 and HyGain commercial antennas use thru-boom button (insulated) construction and work well but $$… Arrow runs the elements through with no insulation; they work but some dispute if they’d perform better with correction factor changes.
I like the WA5VJB “cheap yagi designs” and have built single-polarization versions for 145 Mhz, 222 MHz, and 435 MHz. . Copies of his articles are available at several locations on-line. Use a non-conductive boom (wood (treat for weather exposure if planning a long-term installation), PVC). I used a length of square wood from the local big box home improvement store. If you can’t find a local source for the elements, try SpeedyMetals online (they also cut to length and are quite accurate). They are very easy to build and match. I’ve seen examples online of people making a circ-polarization version. The DK7ZB designs are higher-performance and a bit more exacting to build.
ARRL and AMSAT books and online resources describe how to get circular polarization. With 2 antennas on same boom, easiest is you offset physically one antenna from the other and feed them with identical length phasing harness lines. These lines have to be selected and built to present the correct 50 ohm impedance at the common feedpoint. There is an AMSAT article on the “WRAPS” rotator and antenna system describing how to do this for a pair of Arrow antennas (2M downlink, includes polarity switching). You could follow the same approach with a set of cheapyagis, it is much easier when receive-only.
I use mostly RH-circ polarized on my 2-way satellite station (M2 Leo Pack). RH-LH switching seems to help, however many folks use fixed RHCP or horiz-polarized yagis successfully (I used a single 5 or 6 element “Cheap Yagi” on 2M before I purchased the LeoPack). Polarity switching RH (default) and LH may sometimes help, but I am unaware of any automated means to determine when to switch. So makes more sense for an attended station.
Cross or X? if you mean orientation of elements with respect to a cross-boom, X is considered better if using a metallic (conductive) boom to keep the elements out of the plane of the boom. Same applies to feedline. Keep it out of the way.
I’d build a single polarization VHF (2M) Cheap Yagi of a reasonable size (4-6 elements) on a wood boom (easier to drill), try it horizontal or vert polarized and see if you like the improvement enough to keep going with the project. You can always use it to hit far-off repeaters or for hilltop roving.
73 de KS1G