I didn't expect an immediate response after starting HRT, but I got one!  It changed me profoundly from day one.  In addition to the relief and excitement of finally having it, I very quickly (within an hour or two) was suffused with an incredible sense of calmness and wellbeing.  There's a member here (I think she's a mod, but -- my apologies -- I can't remember who she is right now) whose custom user title says 'mind is quiet now'.  I think that sums it up so well.  For the first time in my life, I felt truly at peace with myself.  The wellspring of stress, frustration and occasional aggression that I associate with testosterone immediately dried up (my partner laughs at the contrast between how I was when I got annoyed before and how I am now -- she also says I'm just a much nicer person all round ;p).  It also made my dysphoria far less acute and self-destructive. 
For the first week I felt an almost physical sense of euphoria, a sort of tingling warmth throughout my whole body.  That faded as things became more normalised, but I continue to feel an enormous sense of peace and satisfaction -- delight, even -- and I find it much easier to relax.  I don't get angry as much, and when I do, it's no longer explosive, it's more like a mild annoyance.  Little things that irritated me before no longer bother me and I wonder why they ever did.  I have more patience.  I am much more sanguine about being myself and not worrying what people think of me, and about facing social situations that terrified me before.  And yes, I am finding that I have some interest in / attraction to men, which would have been anathema to me while living as one myself.  
I realise this might read as pretty idyllic or rose-tinted, but that's been my personal experience so far, and I can only speak for myself.  I am definitely more emotional, and sometimes respond to things that would've annoyed me before by tearing up instead, or outright crying, but that has been a welcome relief in itself given how emotionally repressed I was before.  I find it so much easier and more natural to express myself now.