Proper Velocity $v$ Relative Velocity I understand the proper velocity is the velocity as measured by the traveler, and relative velocity as measured by the observer.
Relative velocity is limited to $c$, but is that also true of proper velocity?  Theoretically, of course, assuming a sufficient energy source was available. And what would be the effects on the traveler if it was possible for proper velocity to exceed $c$?
 A: There is no such thing as proper velocity, considering any motion, the concept of $Proper$ $Velocity$ is very ambiguous. As, whenever you try to quantify any velocity, you need any type of reference frame. And clearly, the measured velocity, is relative to that $reference$ $frame$. It might be the traveler or the observer, but still the measurement of velocity is totally relative.
And any type of velocity whatsoever, is limited to $c$, and proper velocity doesn't play any role at all, it is totally generalized a concept.
And theoretically if, the traveler reaches the velocity $c$, it's relative mass would blow up to infinity, and according the Mass-Energy Conservation law of the universe, anything cannot have infinite mass, and any matter particle can never reach speed of light.
as:  $$ m\prime = \frac{m}{\sqrt {1-\frac{v^2}{c^2}}} $$,
where $m\prime$ is the relative mass of the particle, and $m$ is called the rest mass of that, and clearly for $v$ approaching $c$, $m\prime$ approaches $\ \infty$
and there were one critical $unclarity$ in your question:
You're saying the velocity measured by the traveler is the proper velocity, even if I take that true, the proper velocity of the traveler is always 0. Because, the traveler is measuring his own velocity then.
I hope this made your concept clear.
A: I believe by Relative Velocity you mean coordinate velocity which is defined as
$$v^i=\frac{dx^i}{dt}$$
Which obviously has a limit. And when you say it can not exceed $c$ I guess you mean the speed.
Then by proper speed I assume you mean Relativistic Four Velocity, which is defined as
$$U^\mu =\frac{dx^\mu}{d\tau}$$
And if you calculate it's magnitude you will always get that $U^2=c^2$. That means that four velocity's magnitude can never change
