I wouldn't say the ground plane is required at this frequency range, with normal thickness FR4 the grounding plane of the whole board would be ballpark 2-4pF or so I think, which while it probably wouldn't significantly inhibit operation as it does with some very high frequency designs, it may not be ideal and it probably doesn't have a particular benefit except for shielding.
Though I would also second the idea to use coax. Any wire you use should be considered an antenna, both for transmitting and receiving, and when your working with even a couple hundred MHz if you want a clean signal that isn't radiating noise, you want it in coax. a PCB mount SMA is the standard (and is extremely cheap), but a little ground pad next to a wire for the output would suffice if you were just going to solder coax directly to the board - minimizing the unshielded conductor and keeping the grounded shield as close to the output line should be prioritized.
Not that it really counts, but when you're packing together parts like that, a lot of times it's easier just to put the component designator instead of the value (R1, R2, C4, L2, etc.). You'll probably be assembling it piece by piece with the schematic open, so it shouldn't be too hard to keep track of what value things are, and you're unlikely to need to know the value from just glancing at the board, so it cuts out some clutter on the silkscreen. Many manufactured board get rid of the silkscreen altogether, but I think that would actually hurt putting it together and experimenting with the design.