Buy your SIM at Entebbe. Both MTN and Airtel have counters in the arrivals area, and it takes a few minutes with your passport. Prices and coverage are broadly similar between the two, though MTN tends to have a slight edge in rural coverage around the national parks, which matters if you are heading straight out on safari.
You will need your passport for registration, which is a legal requirement in Uganda, so keep it accessible rather than packed away. A tourist data bundle with a reasonable allowance is usually the best value option rather than pay as you go rates.
Mobile money is worth setting up on day one too, even if you do not think you will use it much. MTN Mobile Money and Airtel Money are accepted far more widely than cards outside Kampala’s main hotels and restaurants, including by many drivers, market stalls and smaller lodges. Registration happens automatically with your SIM in most cases, and you can then load cash onto it at any mobile money agent, which are everywhere, including at fuel stations along your route.
Keep some physical cash as well. Card machines are unreliable outside the capital and larger towns, and not every place takes mobile money either, particularly in more remote park areas.
If your first stop after landing is straight into Entebbe town before heading further afield, our guide on the first day covers useful orientation beyond just connectivity: /first-day-in-entebbe-after-long-flight/. If you flew in from Dubai, /flying-from-dubai-to-entebbe-what-to-know/ has route specific notes worth reading before you land.