Such questions typically degrade into an argument about whether society, in determining its taxation, should be compassionate towards poor people or not. (I suspect you can guess which side I come down on in that dispute.)
My personal favorite alternative means of taxation is a national sales tax that taxes at a rate directly proportional to how incensed the sensationalism-driven general public gets (today) when they see people on public assistance with such items or receiving such services.
For example, practically none of those yahoos gets upset when they see someone on public assistance eating a reasonable meal. So basic groceries, 0%. These yahoos would get somewhat upset about such a person using public assistance to purchase specialty items, like caviar, so such items would be taxed. Having such a dividing line isn't difficult: The dividing line is already drawn in many states, though perhaps the line could be drawn differently. I personally feel that there are too many items in the grocery store that MA considers "taxable" that I believe should not be taxed. But that's just a nuance.
Perhaps, in a system where so much is riding on sales tax, we may need three levels... 0% for basic items, X% for luxury items, 1/2 X% for borderline items.
Public transportation, of course, would be 0%. Regular gasoline for private cars would be 1/2 X%. Tax mid-grade and premium fuel at the full X%. (Full disclosure: I drive a car that requires premium fuel only.)
Clothing up to a certain dollar amount per item would also be 0%, then 1/2 X% for clothing at the borderline, and X% for expensive clothing. Again, many states already apply a dividing line between taxable and non-taxable -- I personally would prefer having that middle-ground borderline category as well.
Essentially, though, "poor" people should have no problem going through their day paying essentially no tax. Items that would be taxed would be items that, for all intents and purposes, are expenses that someone who made other choices about their purchases (what food they purchase; what entertainment choices they partake of; what living arrangements they make, including living closer to work, working in an urban area where public transportation is plentiful, etc.) would be able to readily avoid.
Of course, the devil is in the details: What is "X" in X%, above. I'm not tellin'!
The biggest down-side of this approach is that it stifles economic activity, since folks have more incentive to save than to spend. Right about now, that would be the worst thing we could do.
