Stationary Bikes with MFP connect?

There loads and loads of indoor bikes and smart bike trainers with ANT+ and/or Bluetooth connectivity, the range of prices is extremely wide so you need to decide your price bracket, required features and communicate your intended usage.
I'd definitely recommend getting one with a power meter if you are serious about training for performance and/or want calorie burn accuracy.

What do you use to capture your data from your outdoor rides? (Phone or bike computer perhaps?)

Not seeing why you couldn't use MapMyFitness/MapMyRide) for indoor training though if you already use it. GPS for speed and distance outdoors is replaced by a speed sensor on an indoor bike but with the caveat the resulting speed and distance tends to be very inflated (no aero or rolling resistance etc). An alternative app to MapMy is Strava which can also be linked here.

I use a Garmin bike computer which I link to the indoor bike and then on to Strava but I could link Garmin Connect app directly to myfitnesspal if I wanted to. The bike I use in the gym is a WattBike Pro and I can use my phone with Wattbike Hub training app which also links to Strava but I wouldn't spend anywhere near Wattbike prices for home use, I'd be more likely to put my bike on a wheel-on or wheel-off smart trainer.

Posting to second @sijomial's excellent advice. All around but especially about the power metering part.