My workout plan / need motivation

[BrendanTank]

Hi. So, I'm 235 pounds, but although that may sound like I'm obese, I'm really not. There are several people I know that are fatter than me, and they weigh less, and I also don't even have a double chin or that fat of a face.

I have a workout plan in progress. Starting Monday (I have no access to my weights nor other things, and please do note it's winter where I live and very icy so it'd be hard to go outside and do things) I will do the following:

30 mins on elliptical trainer three days a week
20 mins of jogging two or three days a week
50 reps of bicep curling, 50 reps of triceps curling, 50 reps of laying on floor and pushing weights upwards three days a week (15 pound weights)
20 mins of walking three days a week

I will also restrict myself to 1800-2200 calories a day (I've heard that that can also help lose weight quickly, due to my weight, I should be eating 15x calories of my weight to maintain my weight), I will eat probably cereal / cereal bars / yogurt / fruit in the morning (two combined, not all four), apples / bananas / oranges / grapes for snacks, I usually don't eat lunch when I'm at school, but if I do maybe eggs or a sandwich, and for supper probably a bit of meat and salad.

Does this sound like a good workout plan? I need proper motivation to achieve my goal of 20 less pounds by June / end of June. My final question is, is working out not all about losing the weight, but also the muscle you're building and fat you burn? I'm really not as heavy as I'd sound, but I'd like to be in the same shape my friend is (he appears skinny, but has little body fat on him). Thanks!