Here’s the challenge: you have two parameters - quality and cost. Goal - maximize both. Pick your favorite tipple and tell us what you buy when you are broke but still have taste buds.
My starter - Evan Williams bourbon. I can get a 1.5 liter bottle at WallyWorld for $17.95, which is exactly half what the same bottle of Jack Daniels would cost. Other bourbons are even higher. Evan isn’t Pappy, but it isn’t crap either. The perfect marriage of form.
Yours?
Malt liquor is almost always horrible.
However, Steel Reserve stands at the top of that heap. It’s 8.1% alcohol and it actually drinks like a pretty average beer, especially out of the can.
I was coming in to post about Evan Williams. It’s my cooking/mixing/sneaking into music festivals bourbon, and it’s way better than a lot of more expensive options.
New Amsterdam gin is another bargain.
Smirnoff is acceptable to this vodka drinker. I certainly prefer others straight up, but for the common schmuck mixing with oj, cranberry or whatever its fine.
Leinenkugel’s is cheap where I live, and it’s good enough.
My pick is Ketel One. It’s probably considered a mid-range vodka but for me it max/mins the drunk potential, cost, and crappy taste. Really cheap booze tastes awful or you have to put so much sugar in it that it would give me a sugar hangover, which would be counterproductive.
I guess my second choice would be Pinot Noir box wine. 3 liters for around $12. I tried it once and while it tasted acceptable, it just lacked…well, taste at all. More like ink. It did get the job done though and certainly didn’t have any unobjectionable taste.
George Dickel #12 - not “cheap” in the bottom-shelf sense, but IMO a great value at its (reasonable) price.
Gordon’s gin. If you’re just making G&Ts (as opposed to martinis), it’s just as good as Tanqueray or the other high-end gins, and way cheaper.
Leinie’s is what got me to give up homebrewing, because they were selling Bock at $4.00 a six-pack. Prices have gone up since then, and I’ve moved to California where the only one I can get is shudder Summer Shandy, so my economical beer of choice now is my own: I can make a batch of Bell’s quality porter for about $5 a six-pack.
A bit like Evan Williams, Western Goldis perfectly servicable cheap bourbon available in Ireland and the UK at Lidl.
I mentioned this in another thread, but I got some details wrong.
Trader Joe’s Highland Single Malt Scotch Whiskey, aged 10 years. It costs $25 with tax.
I was never a scotch drinker before. Scratch that - I was never really a real drinker before. I didn’t much like beer, until I discovered that some of the tastier microbrews go really well with certain meals. I didn’t like any hard drinks. If I wanted to get a buzz or to be sociable at a bar, it was pretty much just rum and cokes or screwdrivers for me.
Wine was just a bunch of ridiculous bullshit, from a subjective standpoint. It all tasted like crap to my unsophisticated palate. So all the stuff I’d hear about bouquet and body and undertones and whatnot seemed delusional, and doubly so when applied to the finer liquors.
All of this, until I took my first sip of the TJ’s stuff. Suddenly I understood all of the lurid prose devoted to the flavor of a truly well-crafted beverage. Layer upon layer of interesting and complicated flavor crawled over my tongue, each moment providing a slightly different taste which served as a metaphor for the feeling of warmth as the liquid seeped down my gullet and nestled into my stomach.
I’ve tried a few other scotches, including a 20-year-old Glenfiddich. Most reminded me of paint remover too much, although the Glenfiddich was very smooth and inoffensive - but it lacked the layers of flavor I found in the TJ’s stuff. Having discovered this type of experience this late in life, I feel rather like a virgin who’s just recently experienced what it’s like to be with a real woman.
Dobra for vodka and Rich & Rare for canadian whiskey. Both are real bottom shelf cheapo hooch, but for me are still drinkable neat. That, IMO, is the test for cheap sheep liniment; anything ok mixed in a cocktail. That’s what cocktails were invented for, after all, to mask the taste of awful bathtub gin. So, if you can slurp it down without grimacing with disgust, then it’s decent firewater. IMHO.
Your standards are too high. “cheap booze” and “good taste” are not usually synonymous.
If you just want to get ripped I’ve gotten off brand versions of 4 Loko for 99 cents for a 24 ounce can. @ 12% alcohol that’s like five 12 ounce cans of regular beer. So for $3 one could drink himself blind.
Around here Hamms goes for $3.59 for six pint cans, the equivalent of 8 12 ounce cans. of all the el-cheapo brews Hamms is the maltiest and hoppiest.
Narragansett Lager goes for $4.29 for a sixer of pints. If the suggestion of Hamms disgusts you try 'Gansett. It’s not bad.
Liquor wise I can get off brand rum or blended whiskey for $5.49 for 750ml at the discount liquor store.
YMMV as I’m in Wisconsin and our beer/liquor tax is much lower than other places. If I’d be truly broke I’d ride my bicycle to one of the breweries around here and get my 3 free glasses and move on to the next. And no, you do not have to take the tour if you know what you’re doing.
That’s what makes it a challenge. 
I’m a fan of Old Overholt at $14.99/750 mL (though I know you’re not particularly fond of it). I’m not much of a fan of Evan Williams, but at $11.99/750 mL at my local liquor megastore, it’s actually amazingly good for that price. I’m not a vodka drinker, but another amazing value to me is Luksusowa vodka @ $19.99/1.75L or $12.99/750 mL. I don’t bother, since I like my alcohol to have flavor, but that’s a damned clean tasting vodka, especially for that price.
Just what I came in to say. Since I got beaten to that suggestion, let me throw in Old Grand Dad Bottled-in-Bond. Price is about the same and it’s very nice. Over on one of the bourbon forums I frequent, I could get excommunicated for letting that secret out. It’s the same distillate as the much more expensive Basil Hayden, but with the advantage of not being watered down to 80 proof. Doesn’t have some of the subtleties brought on by the longer time in barrel of the BH, but I can live with that.
There is no such thing as cheap booze in Ontario. Hell, a six-pack of Molson Canadian sells for $9.95.
I drink a lot of high-end beer, but I also buy cases of Genny Cream Ale. It’s always on sale, and I actually like it. With a can cozie nobody knows.
For the efficacious attainment of hangover, might I recommend Olde Frothingslosh, the pale, stale ale?
Glows in the dark, foams on the bottom (YRMV). 
I like Bulleit rye and their bourbon, it might depend on what you consider cheap, but they are very drinkable alternatives to higher priced ryes and bourbons.
I like Rolling Rock. $7.99 for a 12 pack in my area.