I think that given your situation of experience, gear, and weather conditions, a sixty foot cast is excellent. Keep doing what you're doing and you'll catch some fish. After you catch a few fish and upgrade your equipment as you've described in your plan, the better gear plus your growing confidence and abilities will equal greater casting distance.
Be proud! Sure, longer casts will put your fly in front of more fish, but sixty feet to start with is pretty darned good.