You're thinking about it all wrong. Training a few isolated body parts is not only silly, but entirely un productive. Don't worry, no one is going to mistake you for a bodybuilder anytime soon.
You need to work your entire body. Your legs, back and ass are your biggest muscle groups, capable of doing the most work and having the most impact on your overall physique through fat loss and muscle gain.
Do you have any weight lifting experience? You can get a flat bench, barbell and weight set relatively cheap (nearly free if you look for used stuff on craigslist or similar). Add a few dumb bells and a chinup bar and you can do pretty much any exercise worth worrying about.
Even without weights (especially if you are currently untrained) you can do quite a bit.
If you have access to weights and a chinup bar you could get started on something like this
Dumb bell Goblet squat
Dumb bell Reverse lunge
repeat day 1
repeat day 2
You can do abdominal work as part of your warm up or cooldown, or on off days, or before bed or whenever, it doesn't need to be a major focus as all of these exercises will require the use of your abs, obliques etc. as stabilizers.
If you don't have access to weights you could do a single day full body routine consisting of
body weight squats
arm extended planks
You should be able to recover from something like that easily enough to do it every day.
If fat loss is your goal then diet will be a major consideration.