I jump rope for warming up for exercise and training rather than for weight loss. Due to the repetitive nature of it, unless you want to get into a jump rope competition, it's usually hard to stay motivated to do that alone. Use it as a start, but then get a variety of other activities to mix it up so you don't get bored.
For your knees, or other limbs - if they get sore - don't panic, it's probably normal if you are not used to the exercise. Just drink plenty of water to stay hydrated, do some gentle stretching after your work out - and if it's really sore, be sure to have an ice pack on hand to ice the joint. Mild inflammation is not uncommon, so icing for 10-15 minutes will help. Also, schedule down days - maybe work out for 2, then rest for 1 - to allow your body to recover.
If you feel joins are sore, due to weakness - you may want to invest in a brace or Ace bandage for the area(s) - wear them while you exercise to give you some support until the muscles strengthen on their own. Just "listen" to your body - it'll tell you if you are over doing it and when to dial it back.
Don't forget nutrition - be sure you are eating a variety of vegetables and fruits, good proteins to build the muscles that are now working, and carbs to give you fuel for your workout - everything in moderation.
For alternative things to do (some have already been suggested):
Walking - on average, walking 1 mile everyday at a moderate pace will help you (in theory) drop 10 pounds in a year (depends on how consistent you are and if you increase/decrease eating). If you have any state or county parks with trails - make a plan to get out there once or twice a week, start with the shortest path and see if you can work yourself up to the longest path by the end of the summer. Not only is it good exercise, but being outdoors provides additional benefits and time goes faster than walking on a machine indoors.
Eliptical Machine - if you can get your hands on this, it's better than a treadmill on your knees. I feel I get a better workout on one of these than a treadmill.
Dancing - any kind will do (just see how Kirsty Alley change from Dancing with the Stars). I did ballroom myself and like some of the "Stars" from the show, dropped about 15 pounds in 6 months - just due to how much dancing I was doing (classes, practice, and weekly dances) - I was having a blast learning, it was very social, and best of all, it didn't "feel" like exercise. Ballroom not your "thing" or available - then look into others like tap, ballet, jazz, modern, hip hop - anything that gets you moving.
Sports - like dancing - maybe find a sport you'd be interested in learning - most sports have different levels of exercise, and since you'll be learning - you're concentrating more on learning something new vs "losing" weight. So you become surprised when you start dropping some pounds.
Stairs - do you have stairs in your house - then create a little routine where you walk up and down your stairs 5-10 times, maybe twice a day. Add some other things like a few modified (knee) push-ups, and some sit-ups/crunches - and you have a nice quick aerobic and strength routine that shouldn't take long to do - but if you do it every day - eventually you'll see results.
The trick to any of these is consistency. Just like making money on FC - you just have to do a little bit every day, and it all adds up.
Hope some of this helps you out!