I'm on an old 3DS and the Miiverse pages are quite laggy, would it be better on a New system (or maybe being connected to my neighbor's WiFi [My router doesn't work on 3DS systems] maybe won't give me a good connection)
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My old one seems to run it okay.
you can theoretically enable Wi-Fi over 2.4ghz and lower the security settings to WPA2-PSK in your router's settings
O3DS should work fine with Juxt (see other comment), so it's probably the WiFi. If your router doesn't work with 3DS Systems, you'd probably be better off using your neighhbours WiFi.