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So, is using TC under bridge mode useless and out of the picture? Is it better if I just use my regular modem/router? Basically, I want to know if it is redundant to bridge with the TC or if there is an advantage to using a bridged connection to my TC instead of connecting to my modem directly.

If the modem offers a faster wireless connection then I would use that. You can continue to use the Time Capsule as a NAS by disabling Wi-Fi, setting it to bridge mode, and giving it a static IP.
 
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