I suggest FETs that used in LNA designs. For example, ne3514s02 or better.
Must have high gain in required frequency point, because need to make weak coupling. S21 must be enough, to go through weak coupled resonator. There are many papers suggest push-push oscillator or weak coupling for low noise. Microwave absorber above oscillator is frequently suggested, there can be some unwanted RF paths between oscillator and enclosure. Also you can protect oscillator from vibrations with some special "soft" mounting of PCB inside enclosure. Vibrations can modulate frequency that goes through dielectric resonators, diodes or even transistors. Observed by knocking CW oscillator enclosure with screwdriver or by directing very loud music to it.
Usefull literature :
Techniques minimize the phase noise in crystal oscillator circuits
Poddar, A.K. ; Rohde, U.L.
Frequency Control Symposium (FCS), 2012 IEEE International
DOI: 10.1109/FCS.2012.6243701
Publication Year: 2012 , Page(s): 1 - 7
Cited by: Papers (1)
IEEE CONFERENCE PUBLICATIONS
Full text access may be available. Click article title to sign in or learn about subscription options.How Low Can They Go?: Oscillator Phase Noise Model, Theoretical, Experimental Validation, and Phase Noise Measurements
Poddar, A.K. ; Rohde, U.L. ; Apte, A.M.
Microwave Magazine, IEEE
Volume: 14 , Issue: 6
DOI: 10.1109/MMM.2013.2269859
Publication Year: 2013 , Page(s): 50 - 72
Cited by: Papers (4)
IEEE JOURNALS & MAGAZINES
Getting Its Measure: Oscillator Phase Noise Measurement Techniques and Limitations
Rohde, U.L. ; Poddar, A.K. ; Apte, A.M.
Microwave Magazine, IEEE
Volume: 14 , Issue: 6
DOI: 10.1109/MMM.2013.2269860
Publication Year: 2013 , Page(s): 73 - 86
Cited by: Papers (5)