^^ This is correct. With same SSID a device can hand off to a different AP as it roams about a space. Choose different channels, be sure they don't overlap. With a particularly large home it may be necessary to install more than one bridge. I would start with two, see if there is a big loss of speed between the two APs, then consider one in the middle depending on results.
You should be able to auto-connect to a network (SSID) if the client already knows about it. If this is causing trouble broadcasting the SSID until the client learns the network should help. Note though that broadcasting your SSID in an area where multiple networks exist (apartment building, for example) allows for a performance hit each time another device tries to connect. Since devices will attempt to auto connect this could be a pretty big hit.