Welcome to ChefTalk!
People here on this knife forum are pretty passionate about their own preferenc es, so don't be surprised if there's a lot of disagreement. Hopefully, they will keep it civil.
Before any serious recommendation should be made, we should hear something about the intended user(s). So, here goes:
1) This is to be a gift for your parents. Do both cook, or is it just one who does the cooking? If both cook, do they ever do it together?
2) What types of cuisine do he/she/they like to cook and eat? (Asian? Tex-Mex? Haute French Cuisine? Hungarian goulash? Meat and Potatoes? Something else?)
3) How many people do(es) he/she/they usually cook for? What's the largest number of people he/she/they are likely to cook for at a single sitting meal during the course of a year?
4) Do they have a good cutting board?
So, let's start at least with some basics.
Many, if not most of the people on this knife forum really don't prefer or even like knife sets. Buyers of sets are spending a lot of money for a lot of knives, but the per knife value in production and material costs means that these knives will likely be lower value.
Truth to be told, a good chef will end up mostly using three basic knives: as good a quality affordable chef's knife, a reasonably good (but preferably less expensive) paring knife or petty knife, and a serrated edge bread knife. If they're smart, most of the money will be sunk into the chef's knife, and good quality, but less expensive paring knife and bread knife will round out the cutting edges.
But, that's not all that's needed. You need to be able to slow the dulling process and you need to bring the knife back to sharpness once the knife invariably dulls. (And don't believe any "Never Dulls" sales pitch. The only knives which never dull are those which are never used).
So: Basic purchase recommendation No. 1. - A Good Cutting Board. The best are end grain hardwood cutting boards. The big names in mass produced hardwood boards are John Boos and Michigan Maple Block. There are also any number of small-scale board producers (such as The BoardSmith), but at this time, you don't have the budget for them.
The link above is to the on-line store for Michigan Maple Blocks and is for their 15 inch square by 2 inch thick end grain hardwood maple chopping block. Yeah, it's heavy, at 11 pounds. But, it's a solid product and with proper care (read, flood it with mineral oil), it will last decades, giving a good cutting surface that will minimize the dulling of the cutting edges of your parents' knives.
If you are dutiful to your parents, you will have prepped the cutting board before you give it to your parents. Once you get an end-grain cutting board and take it out of its protective wrap, immediately begin treatment. Buy food grade mineral oil (I buy mine from my local Safeway for $3.49 per pint - the least expensive I can find anywhere). Then pour some of the mineral oil onto the surface of the board, slather it around and as it disappears into the grain of the wood, pour more oil onto the board. Keep spreading and pouring the oil until no more appears to be absorbed. Wait until all of the oil gets absorbed, turn the board over and do the same for the back side. Repeat the process as soon as the second side has all of its oil absorbed. Then the next day do another two-side oil slathering and absorbing session. Then wait two days and do another two-side session. Your goal is to get enough oil into the board so that it will not absorb any more oil.
Now, Recommendation No. 2: A Good Honing Rod. Note that I do not say "Sharpening Steel". Honing rods properly align the microscopic edge of your knife - and are instrumental in getting the edge microscopically re-aligned. The best are ceramic. One of the best is the 12 inch Idahone. $32. In using it, DON'T do as Gordon Ramsay does. You don't want to bang the rod against the rod - you only lightly draw it across the edge at a shallow angle (about 15 to 20 degrees) as a "cutting" action which engages the full length of both knife edge and honing rod - and is then repeated on the opposite side. The "cutting" alternates from side to side of the edge on each alternating stroke. Remember: No drum bang; Yes violin swoosh.
Here's a link to an Idahone seller: http://www.chefknivestogo.com/sharpeningrod.html
'nuff said bout honin' rawds.
When even the honing rod won't work, then it's time for a sharpening stone. Try this one: http://www.chefknivestogo.com/kingcombostone.html
You can also order an angle guide from Chef Knives To Go at the same time for 3 cents!
Enough for now - when you can, give us answers to the questions.