General assumptions: Dr. Raymond Valentine should die first, because he walks in locations near the starting points. As always, the game will offer you several methods of eliminating him.
The least original way to eliminate Dr. Valentine is shooting him when he walks between silo's levels. So place yourself near the railing, where guards can't spot you (you can neutralize enemies if there are any). I personally do not recommend this solution, because there is a high risk of being exposed and you will unnecessarily alarm persons in other parts of the location.
Another aggressive method is using a proximity mine or remote explosives. Both objects can be found in a test facility. After obtaining a mine or remote explosives it is enough to plant them on Raymond's route and wait for him to come (try to avoid unnecessary casualties to not lower your score too much).
Personally I recommend arranging one of three possible accidents to kill Raymond. First option is to imprison him in a bomb chamber. Start with using the main staircase and locate a test chamber entrance located on one of upper silo's levels (screen above).
Once you get inside the new room, you'll find yourself accompanied by one factory guards and two scientists, so you have to start using covers right away. You can act here in two ways. If you want to eliminate all characters here then use the computer terminal shown on the above screen to start on a robotic arm. Stun or kill the person who will appear here and then take care of others (if you want, you can leave alone the scientist, who never moves out of his place).
If you do not want to eliminate anyone and just stay in hiding, then distracts people here by activating a radio shown on the above screen. You should decide to do it only after Dr. Valentine comes here, so the radio won't be turned off to early.
Regardless of your behavior you have to wait until Raymond gets inside the bomb chamber. After that, quickly use the chamber terminal shown on the above screen, thus eliminating the scientist. What's interesting - his death will be unnoticed so you do not have to worry about panic among local characters.
Another accident in which Raymond can die, is swapping fire paste for hair restorer. Start with using the main staircase and locating one of two entrances to a chemical lab, located in the middle part of the silo (screen above).
There are two scientists inside the lab, but you do not have to kill him, because they should be busy with work. An exception is a situation, when Dr. Valentine appears in the lab, but in such case you can hide behind one of the lab devices. This plan of murdering Valentine consists of two parts. Start with exploring an empty lab room, collecting fire paste there (screen above).
Now return to the room with two scientists and spike the paste with baldness cure (screen above).
Now wait until Dr. Valentine appears and test the product. The scientist will die in a rather spectacular way, but his death shouldn't alarm Dr. Ashford and other people stationing at the bottom of the silo.
The last possible arranged accident assumes using the mega-taser. In order to do this, you have to go to the special weapons room. You can get there from the main staircase (screen above) or stairs from the side of conference room on the top level of the silo.
Once you get there, start with walking to the records room. You can find there Ashford's notebook and more important - safety codes (screen above).
Return to special weapons room. There are two scientists and one guard inside. Since one of scientists walks over the room, you should think about eliminating him, as well as a guard. After that go to the computer terminal shown on the above screen and turn off the mega-taser.
Wait, until Dr. Valentine appears and gets close to mannequins. Now use the computer terminal again to turn on the mega-taser. If you did everything according to the plan, the scientist will be electrocuted. I recommend leaving the room quickly, because his death may be noticed by nearby characters.