300 lb work out plan?

90% of what you're doing with weights is probably still cardio, to be honest. And there's nothing wrong with using weights in that manner. I would drop the arm workout. You really only need to work biceps / triceps if you are either trying to build muscle on them, or trying to reshape them after you've lost all of the weight you want to lose. In any other case an arm workout is just a less effective cardio workout. Focus your weight work on the biggest muscle groups to maximize burn. Leg day. Back day. Throw some chest and arms in there for funsies if you want, but you'll get more benefit from working the back and legs.

I used to be over 300lbs.

DO NOT START WITH STRAIGHT CARDIO
You can seriously injure yourself. You are bouncing 300 lbs on your legs and ankles after what I assume would be a sedentary lifestyle.

Start out slow, ALL of my doctors (I had fitness weightloss and nutritionists) stated to start out with walking 30mins a day, and once you can get up to a good pace for an hour is when you should introduce light jogging.

Utilize a stationary bike if you want to keep your cardio up higher during this stage! Make sure to stay super hydrated.

I used to be around 250 and when I was starting out I did a lot of calisthenics which helped a great deal. I was able to lose weight without feeling like I was dying like I did with cardio. Now that I'm out of the 200s I'm doing more cardio and not much calisthenics but only because I find cardio (Just Dance games) to be more fun and it's something I can do with my husband.

90% of what you're doing with weights is probably still cardio, to be honest. And there's nothing wrong with using weights in that manner. I would drop the arm workout. You really only need to work biceps / triceps if you are either trying to build muscle on them, or trying to reshape them after you've lost all of the weight you want to lose. In any other case an arm workout is just a less effective cardio workout. Focus your weight work on the biggest muscle groups to maximize burn. Leg day. Back day. Throw some chest and arms in there for funsies if you want, but you'll get more benefit from working the back and legs.

This X1000. When people talk about "lifting" they really are referring to lifting heavy, which no, you don't really benefit from a lot when you first need to shed a lot of fat mass. But it's a great idea to make sure that your cardio program has a resistance component: for instance, working with lighter weights (which I arbitrarily tend to think of as dumbbells up to 20 lbs each), ideally I think in a circuit-training type format with only very very short rests in between sets.

I started my exercise program in the low 300s too. The important thing for me for a long time was really to establish a solid exercise habit, burn calories, and develop some endurance. I used (and still use!) FitnessBlender.com for ideas. Lots of great stuff there. At a larger size I still stay away from any of their HIIT as well as anything else that looks high-impact and might stress my knees. But they have lots of low-impact videos that are a mix of cardio and resistance training in essentially a circuit training format. They'll raise your heart rate, give you a good burn and help you preserve that lean mass.