VHF and UHF antennas
DIY Vertical antennas
If you want a simple omni-directional antenna, it's hard to beat a vertical. Advantageous over a dipole for focusing the signal more toward the horizon, they are simple to build and are usually sufficient for most vhf/uhf needs. There are lots of sites on the internet telling you how to calculate the length of the elements so I won't duplicate that here. My technique is to start with a quarter wavelength for the frequency you want, then connect an antenna analyzer (or in recent years, a nano-VNA) and trim until it resonates where you like.
Here's a design I came up with recently. It uses a chassis mount SO-239 connector with the elements soldered directly on. First I solder on the vertical element, then I solder on a piece of 1/2 copper pipe to go around it as a strain relief. Then solder/bolt on the radials. At the end, I fill the copper pipe up with epoxy. This gives a nice strain relief and has proven quite robust out in the elements. BTW it is important to at least paint the epoxy to protect it from UV.
DIY Yagi antennas
I ran across this design and I think it's really clever - a yagi with no gamma/hairpin match needed. It's designed for simple and quick construction. I've had it up for a couple years and it's worked really well. He has a couple excellent articles on this, search the following link for "Cheap yagi"
Not strictly ham radio, but 1090 is the frequency aircraft use to reply to ground based radar (mode A/C) as well as "extended squitter" mode S, usually carrying ADSB data. This particular antenna is used in one of my gliders to receive ADSB on PowerFLARM for collision avoidance. It's a dipole antenna and while a dipole is a poor match to a 50 ohm unbalanced feed, it's good enough to pick up aircraft within the range you care about. ADSB signals are broadcast with quite a bit of power so even a marginal antenna will pick them up from quite a distance.
The NanoVNA is a great tool for cutting antennas to length. Calculate the lengths to get it close, then trim as needed to nail the resonant point. I think these are so cool - so much functionality for so cheap! Obviously they don't have the dynamic range of a more expensive VNA but it's plenty good enough for a lot of projects.