The primary source of what time-travelers consider paradox is the issue of causality. Effect B must follow cause A. If A does not occur, neither does B. This view of causality is a product of our experience with time. Because we don't see B's spontaneously appear in front of us, causelessly, we assume it never happens. This is similar to early rules regarding conservation of mass. Until we discovered exotic events such as fusion and fission where matter is converted into energy, we assumed all matter must be conserved as matter. Before we developed quantum theory, we assumed that the universe must be Newtonian and an object had to be in one place or another. Before we developed the technology to move mass backwards in time, we assumed that violating causality would cause a paradox.
So, hypothetically, what would happen if we stand in front of a time machine in the 21st century and toss a grenade through to George Washington's boat crossing the Delaware three hundred years earlier. What changes would we notice in the 21st century?
None. We would see no immediate changes from this act. The grenade is causing changes, and those changes will propagate through the timeline, at the rate that events propagate through time normally, one second per second. Changes due to the grenade would not reach the time chamber in the 21st century for 300 years. In other words, you would not be able to visit the grenade-altered 21st century until the 24th century.
What of causality? With the 21st century time chamber perhaps eliminated from the new timeline, how did anyone ever chuck that paradoxical grenade? In short, it doesn't matter. Causality is something we view as law only because we do not commonly observe phenomena that contradict it. The grenade exists in the 18th century, even if there is no longer any cause for it.
What of conservation of mass and energy? Well, matter has been neither created nor destroyed. Yes, a grenade has been eliminated from the 21st century and added to the 18th, but mass and energy have been conserved 4th dimensionally. Matter and energy must be conserved in your available universe, but why must that be in 3 dimensions, rather than 4? There is now an extra grenade worth of mass in the 18th century and one grenade less of mass in the 21st century, but so long as both changes propagate forward, the balance is zero.
So, in conclusion, if you have the capability to return to your home time, any changes you make in the past will never reach you, and you shall never have to face the consequences of your actions in eras you time travel to. Have fun with that.