Personally I just hit the gym three times a week. Concentrate on some steady state cardio like the elliptical which is low impact or jogging, and then compound moevements like squats. I wouldn't focus on primarily one body part as riding requires strength in your whole body, so combine lower and upper body work. It is crucial that you have a strong core or else riding you could start having back and neck pains, so abs and back strengthening exercises are a good choice. Stretching is also a great exercise that will stabilize you on your horse as you acquire a larger range of movement in your joints! It also prevents injury.
Don't over exert yourself though you want to keep most of your energy for when your on you're horse!
Best of luck,
One way we improve stamina with our horses for eventing or jumping is long trots or hill work. Both provide a sustainable and low impact solution for stamina and cardio and often help with top line and other muscle building!