whats a good entry level audiophile headphone amp to start with?
I think that Senns, or at least the model you have, tend to be pretty easy to power so you probably don't
need any headphone amp. But imo every headphone I've had (even the efficient ones) DO sound better with an amp (everyone I've had has been an improvement), but not all can tell the difference or think it is worth it. Again it really depends how much you are even going to listen to headphones and how much you are willing to spend. You might do just fine with a receiver/amp headphone out. I was content with that setup for awhile, but when I did finally get an external headphone amp I was pretty wowed. And that one was about 1/3 as good as the one I have now.
Anyway, I don't know what you mean by "entry level" necessarily; for some that is $500 and up, for others $100. I can say that personally I've had 3 amps now, all under $300 (check the user albums on my profile), and the last one I got is my favorite and I see no reason to replace it anytime soon. It is the Matrix M-Stage and I think goes for $278 shipped. I got mine for $249 before the price hike after the good reviews and "second" version (I think it is virtually the same as the first version or at least sounds the same) came out.
The Matrix is all solid state so if you want tubes then look elsewhere (such as something in the Little Dot line up). I've been running it semi-daily for months now with no issues and love it. It has gain adjustment and easy socketed op-amp switching (to tweak the sound) which are nice features. It's also basically a copy of an amp that sold for around $1000 (Lehman something or other). That probably just shows how much audio gear can be ripoffs more than anything else though (even the Matrix shouldn't cost what it does: the maker is getting a nice profit for sure).
I suggest you look around on Head-Fi for more info on amps:
http://www.head-fi.org/forum/list/5
There are literally dozens to choose from, from home amps to portable. Remember that if you do get an amp and decide it makes no difference or not enough difference to justify the extra expense that you can sell it back and not be out too much. It's worth a try in that sense imo.
do headphones have a speaker break in period like guitar speakers where they sound better after a break in period?
That all depends on whether or not you believe in "break in".

I don't, at least physical break in, because I've not seen any empirical evidence to support it (besides that drivers take a few seconds to a few minutes at most to "break in" when first played...which is probably done at the factory anyway when they test the headphone/speaker to maker sure it works). Psychological break in is a whole other matter: just getting used to the sound over a few days or even weeks.
You, and anyone else, are free to believe whatever you wish about break in and I won't argue it here. I will only say that if you like the sound now that is good because it's not going to get much (or any) better. (Unless you change something else in the chain, like use an external amp).