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u/kevinspaceydid911 - with a $300-$400 budget, I'd probably get a $149.99 Behringer UMC404HD bundle with mic stand and cable, plus either a $199 stereo pair of Rode M5s or a $169.99 pair of Golden Age Project FC4s for your ukelele [Referral Links] - plus a separate MXL 770 (on sale for $69 at B&H) for your vocals.
Both the M5s and the FC4s have a 20-20,000 Hz frequency response, but the Golden Age mics are quieter (17dB A-weighted EIN versus the Rode's 19dBA).
Here is an example shot with M5s.
Here is one shot with FC4s.
Different sound setups, but each conveys a sense of the character of the mics.
Hope this is helpful and good luck with setting up your studio!