Aerobic foundation

I really wouldn't worry about "building an aerobic base", your aerobic capacity will improve to an extent from the interval training anyway.

 

I wouldn't do sprints 3 times a week, especially if you're playing/training for basketball twice a week. Depending on the intensity of the basketball, I'd drop a sprint day and add in an extra strength day.
I'd also take the time to do some recovery work as well. If the basketball is particularly intense you'll need an extra recovery day.

Also, interval training would be an easier transition that going straight into sprints. My personal favourite way to run intervals is a simple 2 min run, 1 min walk, repeat as needed. Something which might be more relevant for you is the 15-20 sprint, 2 minute run, repeat x8-10.
Suicide runs (which I'm sure you've done in basketball and also a great little workout to do at the end of a lighter run.

 

In that case, the basketball would be good for recovery if you keep it at low to moderate intensity (enough to break a sweat and raise your heart rate, but not so much as to leave you feeling drained). I still wouldn't do sprints/intervals 3 days a week. Sprints are a maximum intensity exercise, maximum effort. Done properly they will be incredibly taxing on your body. Twice a week is plenty. Especially when you add in boxing training on top, which in itself is very draining.

 

You'll be lucky to make it the full 10 for a while. You can just up the intensity, reduce the rest. Hills sprints, suicides, etc. Do some enhanced intervals. Add in some bodyweight exercises like push ups or pull ups and turn it into a bit of a circuit. Still, that's some months away. Trust me, just adding intervals will keep you progressing for a while to come.

Honestly, if you're playing basketball (even just mucking around on your own, as long as you break a sweat) doing intervals twice a week, doing two strength days and getting lots of rest you will be fit and strong.

 

Are you an accomplished, experienced boxer?

 

can you fit a heavybag at your place? you could always start shadowboxing and bagging it at home.

soccer?

basketball is excellent. I would much prefer a game with real live people, to playing alone.

swimming is good.

distance runs, if you don't have much else to challenge yourself, push your distance up to 3 miles. Aim for under 25 minutes.

 

Getting your one mile time down isn't how you build aerobic base anyway. For that you want to go for 45 minutes jog.

If you just mean you want to improve your overall stamina before boxing, then trying to run 1 mile as fast as possible is fine, but aerobic foundation/base is something specific and different.

 

Unless you've got your technique down to a T I really wouldn't bother with hardcore conditioning at this stage. Its a waste of time until your sparring hard.