I normally don't like to give out cookie cutter routines. However, I'll make an exception because of the special situation.
First question, Which type of routine do you want? Push/pull - upper/lower - Full body - body part split - and so on?
Thought,
If you goal is weight loss then I would recommend, as most do, a full body. However, I am also very fond of push/pull routines.
Second question, How much weight are you planning on buying?
Now, Here is a very general outline of movements for a full body routine where dumbbells is your only option.
V-ups
db shoulder press,
db bent over row,
db squats*
Push up and/or Dips**
Isolation choice***
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*dumbbell weight restrictions might make this movement to easy. In this case single leg squats or possibly split squats/lunges may take its place. Cycling the use with the above is also a good idea.
**I am assuming you have no access to a proper bench. If you have something that can accommodate your body while laying in a horizontal position but will still allow for ROM(range of motion) of both arms then a db bench press can repla
***This is basically where you can decide any type of isolation movement you want to do. Be it bicep curls, calve raises, lateral raises and so on. What ever you feel like doing, do it. You decide how much you want to do, just don't go overboard and do 100bicep curls lol.ce those.
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Now on a full body the typical rest period is three days a week. Example would be, Mondays,Wednesday,Friday. Basically any 3 non connecting days.
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RSS (Rep Set schemes)
For the initial learning phase I recommend low weight high reps. To ensure you have proper form. This is not for "toning" or anyother false belief. Only to ensure you have learned the proper form so you can train at heavy safely.
Once this is done, and form is ensured to be perfect, Start out with a RSS like this.
V-ups,*
db shoulder press, - 8-12r/3s**
db bent over row, - 8-12/3s**
db squats, - 10-12r/5s**
Push up and/or Dips,*
Isolation choice
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*Body weight movements can be tricky in finding the correct mostly because you have no ability to adjust the weight. So if you are unable to do the suggested endurance rep range. Then start out lower, find the maximum you can do then train at 80% of that. Meaning if you could do 10 only aim for 8 initially. As a beginner should not be training to failure in each set.
**You may wonder why the higher rep ranges, instead of the typical 6-8 many strength athletes use. Well Higher reps with a solid intensity increase lactic acid production. As well as reduce phosphocreatine (PCr) To put as simple as I can, This will increase your oxygen dept (EPOC/EPOE) because the removal of lactate from the body and the replenishing of PCr are some of the prime influences on EPOC, in general.
Oxygen dept,EPOC,EPOE and so on are just fancy ways of saying increased calorie expenditure post exercise to return the equilibrium to the body.
EDIT
Also, you might want to look into super setting. Again another trick to increase overall calories expended.
But remember weight loss is , like any other goal, Dependant on diet. So make sure that is in check
EDIT II
IT is also a wise I idea to change RSS once every now and then. This will help prevent stagnation among other things.