Alternatives that cover everything for DYI needs
- There is no such thing. Whatever you buy now, you will miss something at some point in your DIY life. It may be less obvious than it looks.
My recent example: I was running a conduit in my garage, and was fixing the clips to the wall with screws. The bits that come with my electric screw driver turned out to be too short and the holder for them too thick to reach the screw cap inside the clips. So I used what you would call a duplicate from my hand-tool set. If the hand-tool bits also were too short/thick, I'd have to buy a set of longer bits. And it's OK.
- Even if you do compose a complete set, you will probably miss something at some point in the future because your demand will grow power-/comfort-/functionality-wise.
So it's a good idea to buy what seems to cover all your needs today, and be prepared to spend a little extra if and when you need it. It will not be expensive, unless you will need something very special. But you are guaranteed to not spend unnecessary money on what you may never need by building a "complete" set now.
I've chosen Skil's drill kit and thinking about purchasing a hand tool kit.
What you've found looks very good to me. I have some limited experience with a Skil corded drill/screwdriver, and it was good. Quality/price-wise it's close to the optimum.
You definitely need some hand-tools, and your combined choice looks fine. One thing you'll miss with the Skil set is the water level present in the Bosch set, but it's not worthy paying for the whole Bosch set; just buy it separately. I discovered that my water level (60 cm) is sometimes too short and often too long, so you'll probably need a few of them anyway.
What your set is missing
Obviously we can spot already now what your set does not include (e.g. for electricity, plumbing, masonry work), but it doesn't mean it's bad. It depends a lot on what work you're going to do, so buy those things once you need them.
One thing you may want to consider soon is a vise. But wait till you need it, since they come in very different sizes, and you cannot buy one for all cases.
Also, get some personal protection items, at the very least glasses and gloves. I didn't use them for years, recently started using them and I love this change.