DSLR - Is 23.2 x 15.4 mm a good sensor size?

Nikon D3200. Buying my first DSLR, not sure what to look for.

It's standard APS-C size. You won't get anything bigger in the entry level segment of DSLRs. Bigger sensors are only available in DSLRs of the $2000 category.

Generally it's not something you need to worry about. All currently available entry level DSLRs made by Nikon, Canon, Pentax and Sony are fine.

It is a good sensor size. There are some advantages in image quality of the 24 X 36mm FX sensor. There's a price for FX in weight and money, and really good FX lenses can be more expensive and heavy than DX lenses.
I think that the price of the D3200 might be better spent on the D5100.It has some better features, and the 24 MP sensor of the D3200 will rarely capture more detail than the 16 MP sensor of the D5100.

It's good enough for Nikon and Pentax, who buy them from Sony.

Canon make their own, slightly smaller, sensor.

That size is standard, unless you plan on spending serious money. It will give you more quality than you can generally make use of.