This didn't happen to me (wink, wink) but hypothetically, let's say a friend/relative/acquaintance - who has never been exposed to a high quality system - visited your home, heard your heavily Decware-based system and was BLOWN AWAY by how awesome it sounded. So blown away that now they have to have something like this for themselves and they're peppering you with questions and seeking advice. Remember this is all hypothetical and never happened during the holidays (wink, wink). So, during that interrogation you come to learn that practically all of their musical content is either Apple lossy or Apple lossless files with a few redbook CDs. They're young so assume they're going to start off by just dipping their toe in the tube water with something in the 2-6 watt range, before wading into the deep blue water of Torii Mk4s or Zen Mystery amps. Also assume that the speakers - and listening room - will accomodate a low wattage tube amp, e.g. something from Decware, Omega, Zu, etc.
Based upon my reading of the Decware website, the Mini Torii seems to be engineered for these types of lower quality sources and low resolution files, but I'm open to being educated.
So what amp(s) do you recommend they start with? Also feel free to include any other components - e.g., Zrock, Zbit, Zstage, Pills, ZDac2, etc. - to pair with that amp that you believe would signficantly help that iDevice source and low res files sound as good as possible.

I would tend to agree with Buster, but I do think that starting with the best source you can manage makes it all better. I started my quest with the Zen 2 watt kit way long ago, still have it but am now considering moving it along. Happy listening, Chris.

I do think the Mini-Torii is the amp designed for these sources, but I know so little about these sort of sources that I would hesitate to say that's the best choice. I would think that with the right speakers a Zen amp and a CSP preamp would do the job. . . but as I don't use files and phones and computers and other devices for music that's just a guess. I agree with busterfree that the speaker choice is going to play a large part in the choice of amp. . . .

I would recommend they stay away from a speaker that actually has a "crossover" in it if you're going to drive it with a Decware amp.  Unless you are able to hear the speaker/Decware amp combo "first" before you commit/buy.  At least not a speaker with more than a single cap on the tweeter and perhaps a single inductor on the mid/bass - i.e. a simple 2-way, like the Decware 945 for example.  

I have a Torii III, which I assumed would sound really good with some vintage Klipsch speakers (ultra high efficiency) - no go.  The combination was so bad, it actually sounded "broke".  Plenty of volume, but there was something extremely wrong with the frequency response - I mean awful.  The same speakers sound fine with a SS amp or the other tube amp I have (a Cary).  On the contrary, my Decware 945's sound far better with the Torii than the Cary - go figure...!!!  I was told by a guy, who has been in the speaker design, measurement, modification business nearly his whole life, that the stock crossovers in the ole Klipsch's have a pretty complex and reactive impedance... which SET or SET imitating amps generally are not very good at dealing with.

So I would generally agree with most of the previous recommendations.  Choose the speaker first, but be careful if you plan to drive the speakers with a Decware amp.  I have personally heard most Decware amps, driving most of the speakers offered by Decware either at one of the numerous Zenfests I've been to or elsewhere.  They all generally "work" well, but obviously some combo's are better than others..Depending on the persons preferences and type of music they like.... will dictate what speaker/amp the person should pursue - even within the Decware family.

I have heard, with my own ears, my Torii MK.III driving Decware HDT's, Decware 945's, Tekton Lore S', Omega Super 3 XRS', Betsy Baffles and several different Audio Nirvana full-range drivers.  The results were very good to exceptional with all these.  And these are all minimal or no crossover designs.  Any speaker with a more conventional crossover that I've hooked my Torii to, did not turn out to have good synergy.

Just my own experience and preference.... if you're going with one of the SE Decware amps (SE84, SE34), pair it with the HDT, DNA Horn or an Omega type speaker.  If the speaker has more than one driver, like the 945, ERRx, HR-1's, etc. pair it with a Decware push-pull amp like a Torii.  *note I value life-like dynamics and liveliness.  The Decware SE amps, with multi-driver speakers just don't quite get it up for me - though they sound gorgeous on the other single-driver models.

So... let's throw together a killer system for a nube's first foray into this rabbit hole.  How about a Schiit Bifrost, some Decware DNA horns and an SE34i... pick some decent wires - nothing exotic or made from unobtainium or that cost more than the components its hooked between.... I'm predicting this would get r' done for your "friend / relative / acquaintance".  And be a really nice foundation, in which they could build on, without having to scrap anything going forward for quite some time.