Are you looking to just develop your film, or also develop prints with your enlarger? If you can swing it I would recommend buying pieces individually rather than a kit, simply because you will have more choice in what you actually get, and you can save money by only buying the essentials to start and build up your setup as you learn more.
If you're set on the kit from a convenience perspective, then Ilford so a couple of kits that are fine:
Film Developing Kit: https://www.freestylephoto.com/5470-Ilford-and-Paterson-Film-Processing-Starter-Kit
Considerations:
- Only one-shot chemistry, and no storage bottles. Fine to try out B&W developing but it will be more economical buying chemicals in concentrate and mixing. Recommend something like HC-110 or Rodinal as a first developer as both are very economical, and will likely outlive you. Ilford Rapid Fixer if fine and can also pull double duty for fixing prints.
- No included timing mechanism, so it is worth downloading the Massive Dev app, which pulls data from the Massive Dev Chart. This can provide good starting points for development and can also save your tweaks and adjustments for future use, and can provide necessary timing for consistent developing.
Print Developing Kit: https://www.freestylephoto.com/5750-Ilford-and-Paterson-Darkroom-Starter-Kit
Considerations:
- No storage bottles. Whole developer is generally exhausted after use, your stop bath and fixer are good for repeated uses, so it is worth picking up bottles to save these chemicals.
- No timer. Unless your enlarger has a timer included, which many do, you will need some method of timing your prints. Unfortunately most phones can cause fogging of paper even with filters over the screen, so it may be worth including a cheap mechanical timer to start. Alternatively, you can use a metronome app in your phone with the phone completely covered and count seconds manually. This may cause you to go insane but that's OK if you get tonez.
That said, my recommendation is you haunt eBay or your local equivalent for darkroom sales, I have bought roughly half of my gear used. I would not recommend buying film reels used unless they are clean in photos, as I've had a lot arrive with issues. But things like trays, measuring cylinders etc can be found significantly cheaper.