What are some of the advantages and disadvantages of using a vertical antenna on high frequency? Are there any better antenna types that I should use?
The primary advantages of vertical antennas are that they are omnidirectional, and with an appropriate ground plane (radials) yield a low radiation angle; this reduces the number of "hops" that HF signals must make to reach their destination. Ignoring the ground plane, which might be radial wires or metallic screening buried just under the surface, vertical antennas don't take up much space.
The primary disadvantages of vertical antennas are that they are vertically polarized, which makes them more sensitive to man-made noise when used for reception as compared to horizontally-polarized antennas like a dipole, and that they require a good ground plane to be effective when transmitting.
Vertical antennas for the lower bands require a significant mechanical support; for 80m, for example, a quarter-wavelength vertical antenna would be 66' tall. Verticals can be made shorter with top-loading or various tuning schemes, but at the cost of lowered efficiency -- meaning less of the transmitted signal is effectively radiated.
Verticals work very well near the sea or salt water lake, your ground radials can be minimal and there is a good 6-10dB uplift in your sent and received signal. This is mainly due to much better ground conductivity and lack of obstructions. The much improved ground conductivity lowers the angle of radiation even more and lowers ground losses considerably.
This is backed up by practice and documented in plenty of articles, books and journals. (Look up Naval shore electronics criteria, it's been digitised by Googl)
To get close to this on dry land, you'll need plenty of ground radials. Rudy Severns, N6LF has done some very good empirical research on this. He suggests using around 32 radials and they don't have to be 1/4 wavelength. Source : https://www.antennasbyn6lf.com/design_of_radial_ground_systems/
One advantage of a vertical antenna (not yet mentioned) is that you can hang a vertical wire over a single tree, while a horizontal antenna needs at least two trees. I use my 50 foot high tree for my vertical 80 meter. Yes, it needs 66 feet of wire to tune properly, but I simply bend the wire over the top and then down. Most of the signal radiates from the lower parts of the vertical antenna, where the most current is.
My method of building the antenna was to throw a string over the tree, and tie the wire to the string and pull up the wire, up and over.