I would say that it depends where you get your hamster from - you are getting one from me so I would tell you different things to do on the first few days than if you were getting him/her from a petstore for example, and then again it all depends if the petstore bothered to handle them daily or just gave them food and water and left them to their own devices.
Your hamster is coming to you used to being handled daily, running around in a Roll-around Ball, and having free access to a Comfort Wheel. My guys are fed around 7pm every night as far as possible and water is changed completely on a daily basis. A dilute vitamin solution is used in small 50ml water bottles to save waste. I do swap to the larger bottles (75ml), or give them two (50ml) if I need to leve them overnight. They are fed on Harry Hamster - one tablespoon in a bowl - and a dog biscuit and piece of fruit or vegetable is given every second day. Whatever is in season, just now it is strawberries, blackberries, seedless grapes, this will change to less fruit as winter progresses and I will offer more carrot chunks, brocolli, apple etc. They get various other treats such as pumpkin seeds, millet sprays, tofu and chunks of capsicum pepper a few times per week. Nuts in their shells for their teeth and nails. Fruit branches when available, and bits of whatever is on special offer in the supermarket that week...
Anyway I degress and waffle on as usual
When you pick your little one up I will show you how to handle him/her and show you not to be scared of a baby hamster, as they are completely tame, i.e. they wont bite, but you do need to be confident, as they are like slippery soap, as most of the other guys here will testify to. They are really quite muscular and you need to tire them out a bit before trying to handle them. Hence get him/her out in the ball for fifteen to twenty minutes before trying before trying any major hand to hand work (stick to 5 minutes max for the first week). Plus you also need to handle them somewhere you feel safe that IF they do go shooting out of your hands they wont get lost - I recommend over the bath with an old towel on the bottom for some cushioning, or invest in a large underbed storage tub or playpen, especially if you want the little ones to try and hold him/her too in future.
You want to keep stress to a minimum with a new hamster, as this is the major killer of little ones first away from home. I would work on him/her on your own for the first week before introducing him/her in a big way to the rest of the family. Keep him/her in a quiet location like your dining room or bedroom and not the middle of the family living area, although you can move him/her in there at night to get some sleep
One big tip is to take all the treat bits out of the hamster mix, the sunflower seeds, peanuts, etc. and keep then by the enclosure. When it is quiet during the day (if such a phenomena exists in your house :P ) talk softly to him/her and offer the treats. This will really build up a strong bond between you. Keep to one main voice for the first few weeks but you can share this technic with the others when he has settled in and less nervous.
Try to keep all your major physical interaction to as near 7 o'clock as you can to begin with but as the dark nights draw in you can bring this forward 5 minutes or so per night until you are nearer 5:30pm, and that way the kiddies can appreciate him/her better after their tea before going off to their beds. You have your family routine I am sure, so work around that. In a month you will be able to move the enclosure to a quieter corner of the main living area if you wish or a child's room (see how noisy the wheel is first
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It may be a bit difficult for you to get hold of him/her to get into the Roll-around Ball at first so try to lower it into the enclosure and wait for them to enter, and then when it is time to come out make them come out onto your palm. A little bit of patience and lots of kind words will soon produce the biggest cuddle monster hamster you ever owned.