I answered a similar question in what I hope is a thorough manner.
However, you are asking something a little bit more specific, so let's go about stripping away some pieces: You are discarding any historic or emotional connection to a particular spot on Earth 2.0 (but I will touch back on that in a minute), and are looking for a place that would be beneficial for 5 million to 25 million people to live in (half your proposed population).
The answer actually depends a lot on your technology. If you just grab modern day technology, and the apparatuses to produce it all, you're going to need a lot of people to support production of things (the world economy currently utilizes some crazy economies of scale to produce all the wonderful things you see at your local Blue-Mart). However, if you have this world as a "leisure" world and are providing technology and goods from another source (e.g. warp portal from Earth 1.0) your demands change significantly.
Let's assume you aren't going to just portal in all your stuff, and have to make it, particularly your food, but we will give you the benefit of the doubt and say you have modern GMO technologies (to help adapt to any weird things that live on Earth 2.0). You'll need your capital to be near a source food to ensure you aren't wasting a lot of time and resources on transporting food. Some of the best concentrations of arable land on Earth 1.0 are in India and Eastern Europe. Each of these areas has their own problems, but India has torrential rain, making Eastern Europe a slightly better choice (though India has supported massive populations throughout history). Additionally, Europe provides ample opportunities for expansion, while India is bounded by mountains to the north and the ocean to the south. Both have navigable rivers. India is surrounded by a fault line, however, and may have higher than normal seismic activity. This could be useful (if you can harness geothermal energy in an efficient way) or detrimental (as earthquakes, tsunamis, and other things are more common there than in Eastern Europe).
As a fun fact, the average American farmer with modern techniques feeds 155 people a year.
Another consideration that is a moot point if you are just beaming everything over from Earth 1.0 is natural resources. The kinds of complicated things that go into a cell phone or tractor come from all over the world, with a varying degree of rarity. Glancing at a resource map shows that India is again a decent contender, as it has several kinds of resources, as is South Africa. Like with food, it may be important to place your capital near these resources. As to what is important to your society, that depends on your level of technology. Oil will always be important, if not for fuel then as a component to make stuff (plastics, for example). While competing over resources may not be much of an issue (with only 50m max people) availability and access may be critical to ensuring your industry is running well.
Fresh water is another issue (also sidestepped if you just say desalinization is cheap and effective in your world). India and Eastern Europe have adequate access to fresh water tables for significant populations. Most places in the world, with modern technology, have sufficient water supplies "nearby" for a large population, the issue today is sharing it among 7.5 bn people. Obviously the middle of the Sahara is not a great place for a capital for that reason.
Here's another fun consideration. How are you generating power? If it is all nuclear, being somewhere near sources of Uranium is a good idea. If it is all solar, then around the equator is a good idea, as they get sun all year round. Geothermal? Well, places like Iceland that are built on geothermal hotspots are great.
I know you said nobody would have a connection to a place, but consider this: You are given a blank slate on a new world, what would you do? I'd visit some of the natural wonders and just stare in awe at them, perhaps comparing them to Earth 1.0. Some people may go to religious sites and see what they look like without all the humanity (others might try to recreate their religious sites on the new world. Consider, for example, how would a Muslim person pray on Earth 2.0? Would they pray towards where Mecca would be? Would they make a pilgrimage to the middle of nowhere?)
Accessibility of an area is also important. This makes where your other population centers are important. For example, India might seem awesome in terms of arable land, water access, and other things, but if your other population centers are in Asia, then you have to put roads through high mountains or travel by sea to get there. Not very convenient. However, if you are in the middle of the United States (say, my home town of St. Louis) you have convenient waterways and easier routes to a variety of resources and climate types.
I think you want a temperate environment with a moderate amount of rain. It isn't the most comfortable to live in (steamy summers and snowy winters) but it is where much of the best food growing land is. Your capital can be isolated somewhere in a slightly different climate band, but it will still experience much of the weather swings as the farmland it is near. I'd avoid obvious things, like flood plains and tidal zones, and rely on some "terraforming" to improve the area (draining swamps to reduce bugs for example).