What is a good logic analyser? Surely the $10 can't be that good
Try the $10 first, chances to need something more are close to zero for the projects you plan. A bigger one would be about $100-200 (e.g.
https://www.dreamsourcelab.com/shop/logic-analyzer/dslogic-plus/). It is faster and has more inputs. Though keep in mind that in practice you can not use it at 400MHz sampling rate anyway. The LA has that sampling speed for real, just that connecting probes at that speed would be close to impossible.
I remember first time when I got a DSLogic Plus LA, tried to sampled at 400MHz the output generated with another another FPGA. Almost all the captured edges were choppy before settling to their final value. I thought the LA was defective or something. Well, the LA was working fine, just that I didn't know much back then about impedance matching and transmission lines. The randomly choppy edges I was seeing were because the LA was so fast that it was capturing the reflections back and forth inside the wires. Probes + PCB traces were acting like transmission lines.
I didn't know I had to match the impedances or else there will be internal reflections in the wires, so I've blamed the LA as buggy/defective, for it can't capture clean edges at 400MHz. In reality all the edges were ringing as hell because of the impedance mismatch, and the LA was so fast it was able to capture even those ringings.
Another thing, "Sigrok", which is the software for almost any kind of LA out there, be it $10 or $1000 LA, it is FOSS and supports many kinds of hardware, including oscilloscopes, DMMs etc.
https://sigrok.org/wiki/Supported_hardwareDepending on which oscilloscope you have, might be possible to use it from Sigrok.
Though, the Sigrok drivers for my Rigol DS1054z were not that great, so I never really used Sigrok with the oscilloscope, only with the DSLogic Plus LA (to be more precise, the software name is DSLogic, a fork of PulseView+Sigrok maintained by DreamSource Logic). PulseView is the GUI, sigrok is the command line backend that get the samples from the hardware and run them through a stack of protocol decoders of your choice.