low cost integrated amp for newbie

Although I don't have a specific recommendation (no recent experience with the catagory), I completely agree with your plan of action: You need an integrated right now - you already have a better tuner on hand, and your speakers can wait 'til the next step since they are functioning as intended. It is simply not true that you will not be able to hear differences - even at your price point and with your old speakers - between various receivers or more audiophile-oriented integrated amps. Low-priced gear exhibits just as wide a range of sonic variation as does high-priced gear, maybe even more, though it is of course generally more flawed overall; the only impediment to hearing this fully will be your less-revealing wires and speakers, but they won't render the differences meaningless by any stretch. When I was in the audio retail business, many inexperienced listeners could easily pick up on differences between lower-end amplification options even when powering modest-but-decent small speakers - often to their great surprise (they just hadn't ever really listened before - hadn't thought they could or needed to). Welcome to the site (and to the hobby?), I hope you enjoy whatever you get out of it, including your new amp.

Fishinfool's advice, while not totally incorrect as far as it goes, to me seems a little beside the point, considering that any major future system upgrade (if Ann decides to go that way) will likely mean improving upon any small integrated amp bought in the circa $300 range, no matter what she chooses first at this juncture. That is, after all, how better systems are built over the years.

Since I really doubt she will be in any danger of trying to mate, for the moment, a particularly 'tough load' speaker (read: larger, maybe esoteric, more expensive, and more revealing) with her modest amp choice, this 'danger' can be safely disregarded for the time being. Any decent small integrated she is likely to get should do an appropriate job of driving any decent, small, and relatively inexpensive speakers she might pair with them as her potential next step.

Yes, it would be ideal to be able to choose a new amp and new speakers concurrently and audition the options together as a system to create a synergistic match with no prior constraints, but her amp is on the fritz now, and she's just getting her toes wet in this stuff. Significant further upgrading, should it occur, would mean eventually upgrading everything anyway, small integrated included. But she will not be unduly limited in her choice of matching speakers in the commensurate size, price, and fidelity range she is likely to be shopping in this time around by choosing her amp first to meet her current needs, so I wouldn't encourage her to needlessly worry over having to go 'amp-first' now.

However, I do concur, as a general rule and when other conditions (such as a broken amp) are not prevailing, that if and when Ann decides to progress higher up the audiophile food chain, the ideal upgrading sequence is speakers first, amp to follow - though as in everything audiophile, there is hardly universal agreement with that view. But even in that scenario, the amp she gets now will probably suffice to produce acceptable sound for the meantime if she has to stagger her upgrades and go speakers first, amplifier second in the next round (even if that round winds up beginning with her next speaker purchase and not a subsequent one). Besides, I suspect her next moves, beyond maybe changing the present speakers, would be in the areas of sources and wires, and anyway, one of the beauties of buying on Audiogon is that she will not be facing much depreciation when it comes time to sell the small integrated (especially one bought in the price range she is contemplating here), so the whole prospect should be neither daunting nor painful in the pocketbook at this stage of her audio-development.