If you do wind up flying into Basel - and I agree that you may well find it easier to use Zürich, but a bit more info about your plans would help - it is straightforward to get from the airport to Luzern.
There is a bus stop right outside and the number 50 takes you right to the main station in Basel (Basel SBB). From there a frequent train service straight to Luzern.
If you change to landing at Zürich it is even easier - the station is right at the airport and trains go right from there to Luzern. Direct trains alternate with trains which require a change of train in Zürich HB, the main station. If you don't want to change trains in Zürich just wait a few more minutes for one straight to Luzern.
Whichever way you choose, when you get to Luzern it is really easy. The station is a dead end one so you don't need to be in a mad rush to get off, and many trains terminate there. All the tracks are on one level. Downstairs are the toilets and lockers. Restaurants and other food are on the main level, up a floor and down a floor in the passageway to the city. Buses and ships and the front of the station are all on the same level. You are very close to the old city.
To get to Basel, just return to the station and take any train to Basel SBB.