This may a bit TL/DR, but here are my own, personal choices and reasons thereof:
Masoli, Jeremiah, QB - Keep. He may have played himself up a rung or two recently.
Lewis, Jeremy, OL - Keep. He was a very good OT until he was injured.
Figueroa, Joel, OL - Gone. While a good OT, he has had too many injuries the past two seasons.
Olson, Jake, OL - Keep. With all the injuries on the O-Line, we need backup INT OTs (at least).
Madu, Jr., Mossis, RB - Gone/sign for less. The injury bug did nothing for his value this year.
Sinkfield, Terrell, WR - Keep. His pros vastly outweigh his cons, and Zach looks VERY comfortable passing to him.
Grant, Bakari, WR - Gone. While often injured, he takes FAR too many preventable penalties when he DOES play, and his lack of production is not worth the headache of another FA battle.
Hickman, Justin, DL - Keep.
Hall, Bryan, DL - Keep if possible. While he's a monster at DT, we have MANY quality Nationals that can play there.
Harris, Erik, LB - Keep.
Caldwell, David, LB - Not sure. I haven't seen enough to know if he can be a starter.
Reed, Taylor, LB - Not sure yet. He may be looking at the NFL again, but his stats/performance this season haven't helped his cause.
Stewart, Brandon, DB - Keep. Last year, I would have released him, but he certainly picked up his game. In the very least, he is a veteran depth player.
Gainey, Ed, DB - Gone. He is very replaceable.
Davis, Emanuel, DB - Keep. Probably our best INT DB.
Carter, Jalil, DB - Gone. He is very replaceable.
Sears, Jr., Johnny, DB - Gone/sign for less. Too often injured, but when he CAN play, he's a monster.
Medlock, Justin, K - Keep. Spend the money on Money!
Prime, Carl-Oliver, RB - Gone. Was primarily used as a blocking FB/TE and not much else.
Aprile, Giovanni, WR - Gone. He has done virtually NOTHING since he signed, and Coates is better.
Fantuz, Andy, WR - Gone/Sign for less. IMHO, Fantuz has spent more time in the IL than he's played during his stint as a Ti-Cat. IF Austin re-signs him, it should be for a HEAVY incentive-laden contract (games played, receptions/yds/etc)
Gascon-Nadon, Arnaud, DL - Keep. Capable backup DE, and a great ST player. Might be able to challenge for a starting spot if Norwood's knee isn't ready in time for TC.
Ellefsen, Everett, DL - Not sure. He was a backup/practice squad player this year, and didn't do much when he DID play. Better minds than I might be able to expand on this.
Hazime, Hasan, DL - Gone. Unfortunately he was too injured (recovering from Achilles tear) and couldn't crack the backup roster.
Laurent, Ted, DL - Keep. No-brainer.
Bulcke, Brian, DL - Gone. He had, I think, exactly ONE complete season out of his THREE years here. I would only re-sign him if we can't sign Laurent. Don't forget that we have Gaydosh signed to an extension.
Atkinson, Michael, DL - Keep. He may challenge for a starting position.
Plesius, Frederic, LB - Not sure. His price tag may be too high, but probably worthwhile if Taylor Reed doesn't sign.
Edem, Michael, DB - Keep. We need a good backup NAT DB.
Stephen, Courtney, DB - Keep. He had an All-Star season and was the team's nomination for MOC.
King, Neil, DB - Keep. We saw just how valuable he was while Butler was injured.
Miller, Kyle, DB - Gone. We have too many NAT Safeties as it is.
Crawford, Aaron, LS - Keep. These guys are gold.
O’Neill, Hugh, P - Keep. He's a VERY good punter, and it would allow Medlock to focus on place-kicking.
In summary, the players I'd let go are Figueroa, Grant, Gainey, Carter, Prime, Aprile, Hazime, Bulcke, and Miller. I'm not sure about Reed, Ellefsen, or Plesius; and I believe we should let go/sign for less Madu, Sears, and Fantuz. Madu because of injuries, lack of production and Ford is a better runner between the tackles; Sears because of his injury history; and Fantuz for the reasons I listed and more.