Hook the 625 up with a yellow RCA cable to the tv for video. Hook the blu-ray player to the tv with an HDMI cable. If you have a sound system I would connect the sound from the 625 and the blu-ray player to that.(best sound)
RCA Cable for Video!! ICK!!!!
Your TV may also have an SVideo port.. if so,
that is a much better video solution than the RCA video.
If you have an AV receiver (tuner, amp, video switching) then you may have an option for "Upconversion" from SVideo to HDMI .... so if you plug the SVideo into the A/V Receiver it might "up-convert" to HDMI ... and then plugging your Bluray into the A/V receiver as well as Dish and any other audio & video devices, would give you the best switching and connectivity options ...
When I had my 625 ... I had the SVideo going directly to the TV (4:3 standard 36 in tube) with the RCA Audio L/R feed, and the Optical Audio going to the receiver .. thus I would have high quality audio when I wanted but I would always have high quality video. (ie. power savings, rather than always needing to turn on the receiver to get video/audio to the tv.
and one of the main reasons I've always loved receivers that have two sets of TV1 outputs)
As now, I have a 722k, HDMI goes direct to tv, Component goes to AV receiver ... though I could reverse that at any time... I've just never needed to... And if you don't have an AV receiver it might be worth the addition.
even used from Ebay .. I picked up a 4 year old model Onkyo SR804 for 125 delivered! in 2007 it was msrp 800 ... which meant it should've been online for 500 or so, and given time and someone else's desire to upgrade (they wanted 3d and more hdmi ports on their receiver)
Anyway.. use the highest quality video standard that your TV supports.. if it doesn't have SVideo then you'll have to live with the composite (rca)