I want to put in a raised garden bed what is the best but cheapest way

There are so many choices. When you say best but cheapest, I understand cheapest, but best is... well it depends on your point of view. For all of the choices as long as you can get the garden to sit fairly level and stable (not wobbly), you put them on top of whatever is there, no worries about moving rocks (and yes it would be good for drainage)

For instance, do you just want it for one year, don't care what it looks like, as long as it works to grow the garden well.

Do you want it to look terrific, but maybe not so cheap.

Etc?

How tall do you want your raised bed (separate from size LxW)?

NOTE: For an ideal raised garden you want the maximum length or width (whichever way you look at it, in one direction anyway) to be no more than 4 feet (which is the farthest you can potentially reach across).

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Really cheap, doesn't look great, doesn't last multiple years, but really does grow things well:

Bales of Straw

I know sounds weird right. But you get bales of straw (NOT hay - do NOT want seeds), keep them bound with their twine. Set them out to be your new garden beds. https://www.gardeners.com/how-to/straw-bale-gardens/8882.html

I did this for a year (skipped the nitrogen steps, just made space in the bales, added soil and plants) and had a fantastic garden, plus no worries about rocks or digging or ground prep. Although I'm sure it would have been even better if I would have taken the time for the nitrogen/decomposition step.

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Pretty cheap, looks...uhh okay I guess, supposedly works great, durable???:

Fabric raised beds. They are made out of what looks like a sort of felt/cloth, I've only seen black, see them at garden centers (even Fred Meyers), come in variety of sizes. Put them where you want, fill with soil, plant, enjoy

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Sort of cheap, looks....varies, works well, usually at least a few years:

Plastic. You can go really cheap and use 5 gallon buckets (from any home improvement store - like Home Depot), drill holes in bottom, can add filler for bottom (if you like), add soil, plant and enjoy. Can go more expensive and get plastic planter boxes, and containers. Again, fill, plant, enjoy

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Expensive, looks really nice, lasts many years:

Wood. Usually the best would be cedar, no worries about ground contact or chemicals from pressure treated, or chemicals from railroad ties, etc. Can make the whole thing out of wood, or get plastic or metal brackets to form the corners (if you aren't great at building things). Or you can buy them already built for you.

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Most Expensive, can look really nice, lasts pretty much forever:

Stone/Cement/Concrete/etc. Can make forms and pour concrete. Can use cinder blocks (with mortar, or without), fill with cement/concrete/rebar/soil/etc. Can use pre-cast retaining wall stones (at garden centers, and big box like Home Depot), they can usually be stacked dry. For all of these you will need to make a base of stone that has been dug to the right depth (to avoid frost heave), and compacted well (to avoid sinking later).

Good Luck

You can place your box for the raised bed on top of the rocks. Just make it as level as you can. Best is seldom the cheapest and you have to decide what you are comfortable with. Cedar planks, if available, are great but expensive. Construction lumber carries no treatment but outdoors you should only expect a couple of years before the wood starts rotting.

Treated lumber works well, but many people don't like it because they think that the copper used in the treatment can leach out and be absorbed by plants despite evidence that it does not. That is what I used for my gardens that grow green beans and asparagus.

You are building a four-sided box no wider than four feet and as long as you'd like. I made the ends of mine interlocking, like Lincoln Logs, but you can use steel "L" brackets at the corners to hold them together or 4x4 posts in the corners and screw the sides into the posts as I did to make a friend's planter. Best of luck.

Home Depot sells the corner bricks that have grooves which perfectly hold a 2X4 for about $5 each. We used weed barrier in the bottom and poured our bags of garden soil and compost on top of that to the tops of the boards. For an organic garden, don't use pressure-treated lumber as it has a chemical treatment. We used regular 2X4 boards and they are just fine after 3 years.

https://www.hometalk.com/search/posts?filter=raised%20garden%20bed

Use concrete blocks which will last forever.

https://getbusygardening.com/concrete-block-raised-bed/