Which Blu-Ray Player to get-Component and HDMI

[markw]

In the past I have had a Sony PS3 for Blu-Ray on my living room TV and also a HD DVD player on that plus in my bedroom a HD DVD player that is connected to a XBox 360. Since I got HD DVD rentals from Netflix I only owned one HD DVD movie. I've been watching it play out with studios going to Blu-Ray. I am watching to see what Warner Bros. and Paramount does but I think it's just a matter of time for legal issues to sort out and them change. I know Blockbuster is Blu Ray only and with Netflix going Blu-Ray only I took the step to go Blu-Ray only. All my HD DVD gear is for sale on ebay now. I figure in a worse case if the tide turns by then I can put my money into a much better HD DVD player.
Well enough of that. I've decided I'm going to put my money into a nice Blu-Ray player. I have an entertainment room that I plan to put it into but I want to also wire it to the TV that's in the bedroom. I already have component wiring running from the entertainment room to the bedroom. My idea is to get a Blu-Ray player with a infrared remote, hook the HDMI up to the entertainment room TV, run the component to the Bedroom TV. Are there players on the market that will output both at the same time?
If not, another idea I have that I'm open to is running HDMI to both so do any have dual HDMI outputs? If so this is a huge plus to me. If not are there any good splitters that I could hook the HDMI output to that then gives multiple HDMI outputs? It's important that it also has multiple digital optical and rca audio outputs. I plan to use one of those Remote Extenders for Remote Control. I don't want to put too much money into one but I know there were some issues with the early generation Blu-Ray players and wondered which ones that are currently on the market are the best. I prefer to spend less than $500 and even less if possible.
Also, since I have a large Standard DVD collection it's important that it does a good job of upconverting standard DVD's. It's also important that it can play DVD-R's since my whole home video collection is on DVD-R's