How does the Miller effect affect a JFET-amplifier stage with tuned-circuit input?
I wondered if Miller effect has any impact here, as it will lead to a
  capacitance between JFET's gate and source


Miller capacitance is between drain and gate but for JFETs you can usually find types with about 1 pF so go for something like an 2N5486. 1 pF multiplied by voltage gain could be somewhat troublesome at 30 MHz but not at 1 MHz because Ct is going to be several tens of pF to hundreds of pF.

Try it and see and also compare your design with one on the internet using JFETs.