If your new TV has a coax RF antenna input you no longer need the converter box. Connect the antenna to the TV, set it to over the air, and scan for channels. If it doesn't and your box has HDMI out then use that. If it doesn't have HDMI then it won't output HD. You want one that does.
The BD player will play your DVDs and CDs so you don't need the old CD/DVD. Connect the BD player to the TV with HDMI. TV sound is pretty poor so using the built in TV speakers for music doesn't sound acceptable to most people. If you get a soundbar you can connect the old DVD/CD player directly to it with a stereo audio cable. You may need one with a 3.5mm stereo mini plug on the soundbar end.
The VCR has a composite video + audio output. Check the TV...