So... joystick basics...
Joysticks can be fundamentally divided into two categories: digital and analog.
Digital joysticks are basically sticks attached to swiches. Push the stick and it activates a switch. The only possible values are digital - on or off. This is the cheapest and simplest type of design and was what Atari settled on (using a DE9 connector the same as used for serial ports). Most 8/16-bit home computers used digital joysticks, generally with Atari pinout, sometimes (MSX) with enhancements or with an intentionally modified pinout to break compatibility (Amstrad 🙁 ). These sticks tend to be best for arcade-style games.
Analog joysticks measure how far you have pushed the stick in a certain direction. The value is an integer on each axis. These sticks are more complex to build and tend to need calibration. This became the standard on PCs, using a DA15 connector (same as used for AUI networking transceivers, but with different retention mechanism). These sticks tend to be best for flight sims/space sims. Later analog sticks use USB, but no DOS support there, so you need the older versions.
It's possible to get adapters to attach digital sticks to an analog port or vice versa, but the result is rarely satisfying - analog sticks are hopelessly imprecise for games expecting digital input and digital sticks offer no nuance as needed for games wanting analog input.
Instead, gamepads became popular on the PC. They connected via the same analog interface but used hard digital signals. Gravis at one point tried to make a dedicated digital standard (GRiP) but it failed.
TLDR: you have DOS PCs. You need joysticks or gamepads with DA15 connector. If you play a wide variety of games you need both, as analog sticks suck at arcade and gamepads are no good for sims.
As for specific recommedations - it's all very subjective. I like Gravis products; I lusted after the Gravis Phoenix in my teen years (when it was far outside my budget). It is still considered one of the best sticks for Wing Commander/Tie Fighter, but I hear bad things about reliability/durability, which 25 years down the road isn't exactly what you want to hear. The Microsoft Sidewinder3D is less over-the-top, but is rugged and does the job admirably in all its versions I've tried so far. In terms of gamepads I like the original Gravis GamePad (and NOT the GamePad Pro) in all its square NES-styling but you'll find differing opinions on that one - and I'm first to admit I'm not a huge arcade gamer in the first place.
Oh, and last word of warning: specific joystick interfaces can be (CPU) speed sensitive. If your analog joystick completely refuses to work or seems to go crazy, your PC may well be too fast for it. I've not found any clear logic to which ones are problematic and my oldest game card (a dedicated 2-port joystick interface from 1990) will work on any system I've stuck it into.
