Reddit mentions of Spyderco Spy-DK Lightweight Non-Locking Notch Joint Plain Edge Knife, Black, Left/Right

They actually make a knife specifically for Denmark: the Spyderco Spy-DK Denmark legal EDC

Ok, you're welcome, well I don't know how flexible you are on the outside appearance of the knife, but you can still get a great folder.

For a super useful performance knife, I really like the Spyderco Pingo

For a cheap knock about knife that is also very useful but you won't be too worried if you break it, lose it, or get it taken by police...I like the Opinel #7

For overall utility, I like a classic Swiss Army Knife.

Then you have a bunch of varied designs that might work for you. The Higo No Kami, the Kabar Dozier, the Spy-DK, the American Classic Case Sodbuster (I recommend the Jr. size).

And you can easily add a clip to any of these.

A little late to the party... You are following the same trajectory as me. I'm just now expanding into fixed blades, but before you put the brakes on budget folders you should check out a few more options.

The Coast FX350 (9cr18mov, G-10, frame lock, 3-position clip) is a beauty for under $20. The BX315 (9cr18mov, rubberized handle, lock back) is great for wet work and is currently selling for just under $15—it has a sheath instead of a clip because the large rubberized grip doesn't slide in and out of pockets very well. The BX315 also has a little brother, the BX300.

If you like the Kershaw Link's profile then you should try a Flock (8cr13mov, FRN, tip-up clip) that's going for $15. It is a dealer exclusive that was poorly marketed and escaped most people's notice. Probably one of the best Kershaw deals going right now.

Spyderco's Spy-DK is currently selling for $30. It's a special non-locking model for Denmark knife laws. It's old school slip joint action but you get a N690Co blade that is a step up from their more expensive budget folders.

Back to fixed blades...

As I mentioned in another comment, Schrade is a good place to start for budget fixed blades—check out the SCHF36 Frontier for under $30. One thing to note is many fixed blades in this category are going to use 1095 steel which typically requires some maintenance, but most are powder coated to address this. Don't let 1095 scare you away from some nice options.

Now, I know you are looking for budget knives but there is a mid-range option that you may want on your wishlist. If you have an Ontario Rat folder (which you should) then you might want to compliment it with a Rat 3, 5, or 7. Like I said, I wouldn't consider Ontario fixed blades as 'budget' but they're a bargain compared to brands like Tops.

I hope this helps and have fun exploring, this rabbit hole runs DEEP.