Newbie Power Cord Question

It's true. Power cords are expensive and seem less influential
than most other cord types. However, an Acoustic Zen El Nino should be about a hundred dollars used and it probably will make a very slight improvement in the sound of your system. Also, as long as it is good condition, a used cord is always a better option. They don't need break in and will always be cheaper. New power cords, and I have spent thousands on them, just don't justify their cost. Have you tried a power conditioner? There are some on the market that would prove a more cost effective power grade than a power cable and they can serve to improve the performance of other components in your system as well.

You don't give us enough info to give informed advice. What kind of integrated amp? What comprises the rest of your system? Power cords, like all wires & cords, are system dependent and there's no "one size fits all" answer. If your system is of sufficient quality and resolution, you may gain great advantage with a new power cord. You might also find it a waste of money in the context of a different kind of system. For what it's worth, I found power cords to offer more bang for the buck improvement than any other cable upgrade. But that's just been my experience. Obviously, others have had the opposite experience.

Photon46 makes some good points; more info would help. Given the available information, a used Synergistic Research AC Master Coupler might be a good entry point. They're well designed, well made, heavy gauge and a near classic. (Can a power cord be considered a classic?) At very least one would make a good baseline for comparing other cords. Google the name for reviews. You'll see them being sold regularly on AudiogoN for ~$140.

Try the cheapest but best secure feeling cord that I tried for a sense of what might be the end result of switching.
Since then my expense budget for cabling went way up.
My favorite cord now however will almost certainly reach your limit or be a bit more. I now use the Audience Top O the Line AC cord the equivalent of the Au 24.
The best cheap cord to try with little risk is just a few bucks. It is the "Absolute Power Cable" from GTT audio. A simple but very well made cable with very good terminations. I think they are continually available for the special sale price of $49.99 ordered directly.
If you suddenly get rich use a continuous cast Ohno sigle crystal cable by Vampire or Neotech amonst others. If you want to get your Significant other hysterical I like the whole Cardas Golden anything, but expect a certain warm coloration and have a strong rationale at the ready to calm her down.
The best resource is the lending library of used cable is available from The Cable Company used cable division. They can steer you into a cord to suite your taste with an incredibly comprehensive knowledge base.
Good Luck but I think your ICs and speaker cables make the biggest change. Power cords are only as good as the power they are fed and if you have "dirty" or wavering voltage you really need a good conditioner and dedicated lines. However that propostion will run a log more dollars than you have in your budget.

The PS Audio Xstream Plus SC is made of single crystal(continuous cast) copper, and won't break the bank at about $150.00 used. You have to be fast when you see one come up for sale though(they sell fast- there MUST be a reason). (http://www.psaudio.com/ps/products/detail/xstream-plus-sc?cat=power-cables) You can't go wrong with this one.