The very cheap ones (eg
https://www.ebay.co.uk/itm/176694391820) work fine for I2c, though may struggle with higher speeds. They're based on the same Cypress ezy-usb chip as the early Saleae devices and a heap of other designs.
These are well supported by the Sigrok software. Other more expensive devices may come with their own software, sometimes copied from Saleae or Sigrok.
There's also one based on an RP2350 which looks good but works in a slightly different way, storing the data internally rather than streaming over USB. It's fairly new and the author is active in supporting it.
I agree with Psi, you will have a lot of data and the ability to pan and zoom freely on a large screen is important.
Some oscilloscopes also have I2C decoding and may offer zooming. One older model, the Yokogawa DL1540, allows for the printing of a very long zoomed-out trace on the built-in printer. This was the first method I used for debugging I2C some years ago! However it's still a short trace compared with a logic analyser and doesn't decode - you have to work it out manually.
The advantage of an oscilloscope over a logic analyser is that it shows up invalid logic levels. These can be difficut to find with a logic analyser because the logic analyser only records a digital value and may not pick up the same value as the device itself. An exception to this is the later Saleae devices which are not just logic analysers but multi-channel oscilloscopes recording actual voltage (at lower capture rates). This partly explains their price.
An older logic analyser such as HP or Tek has some uses but often won't have decode software for I2C and may have rather limited capture length. They're better for wide microprocessor buses and not so useful for I2C or SPI. Newer models will cope but at a cost.
If you want to look into that option I do have an old Philips I'd like to get rid of.