I wouldn't keep *any* netbook on my lap for an extended period of time.
I'll just echo TiNman and the EIB. Hit the stores and see what you like. On Media Player, yes, if it's running Windows (XP, Vista, 7, whatever*), it'll have a version of the Player on it.
Not sure why you were warned away from the HP. I know ThisIsNot for one is a fan of their Mini. I work on an ASUS 900, but the Mini looks good. I like the larger keyboard HP has.
My hands are small, so the size of the 900's keyboard isn't that bad for me. I am writing most of my book (I'm a professor) on it. It's not the most comfortable thing, but it isn't the size of the keyboard that is the issue, it's the silly position of the right shift key on ASUS keyboards.
The ASUS 900 and 901 models have, I think keyboards that are 89% (or maybe 86%? I can't remember the exact number) of full size. HP's and MSI are I believe 92%, if not larger. I know I can tell the difference when I play with the MSI at the store. The 9" models are phasing out, but I believe Melbourne has the ASUS 1000 series out there, though not sure where the price is right now.
As for battery life, I understand the desire for longer time, that's always a good consideration, but consider how much time you may really be on battery versus times you can find an outlet. Whenever I'm traveling I've found that I'm on an outlet easily 90% of the time, making the 2+ hours I get on my 4-cell battery usually more than enough (More than 2 if I turn off WiFi).
I don't remember if you said specifically, but where are you traveling? Are you going overseas (in which case, do not forget to get an adapter, perhaps one with a transformer for the various outlets in different countries) or just walkabout in Aus? (I did the latter. Finished my PhD in the US and got to spend 6 months in Australia. The wife and I loved Melbourne, one of our favorite all-time stops. Even went to see the Fairy Penguins come back to shore
*Even if it was running Linux, you could, with tweaks, run WMP on it, but there would be little reason to do so.