As mentioned by the topic starter, an idea regarding F-18 or Grippen looks very reasonable. Either one of the most reliable companies in the world in that business segment (which they have experience with), or a neighbour (that might be transparent for them to a large extent).
And I do not see any "militaristic" aspect here at all. If they were really afraid of "Russian invasion", they would spend their budget to buy PAC-3, MLRS (against "invading" land forces), Javelins, Apaches and so on, but not fighter aircraft as they cannot intercept modern (or yet to come) missiles and munitions. Looking at the map one can easily see that Russian AF do not need to enter their airspace to strike. Are they (Finns) going to enter ours? I don't think so.
IMHO the reality is that their current fleet is running out of lifespan and a replacement is needed. Nothing more. If they have AF (and not a bad one), they prefer to keep it at a certain level to maintain a certain status.
For Russia, the best option would be their purchase of F-35. Would be a great complimentary add-on for training of radar guys :-)