They're not the cheapest (though not the most expensive either), but take a look at the APEM Multimec line of tactile switches. I used them in a project, in large part because they exist with LEDs, and have a large selection of keycap styles,
and different length keycap extenders to raise the cap to the perfect height. I like the milky white caps and the black-with-clear-dot caps for backlighting with LEDs.
In Europe, Reichelt.com has the Multimec 3F series at good prices (and more importantly for my application, where cost is a factor, you can add the LED yourself, which is what we did because APEM charges way too much for white LEDs), so we used those. I think the 5E series was a tad more expensive. But this was during Covid, so that may have impacted pricing.
Anyhow, take a look at
https://www.apem.com/idec-apem/en_US/PCB-switches/Tactile-Switches/c/Tact_switches?page=1 Each Multimec series' page has a list of compatible keycaps.
Actually, you may want to flip through
https://blog.apem.com/en/page/brochure-mec-products first
These are tactile switches, however, so may be clickier than you want. "Cheap and hard to press" is not really a thing: a button is too hard to press when it is not correctly selected for the application. All else held equal, big keycaps need buttons with higher force, small keycaps need lower force,
even if the switch inside is the same size. The ideal force also depends on the weight of the device it's in (you don't want so much force that the device slides away), the application (tact switches are great for controls, but terrible for keyboards, for example), etc. So "cheap and hard to press" simply means it's a device with poorly selected switches, not necessarily poorly made switches!
(The Multimec 3F are around 350g of force, so definitely intended for big keycaps, which is why the smallest cap they sell is 6.5mm diameter, but most are 9.5mm diameter and up.)
If you really want smooth and not clicky tactile, look at actual keyboard keyswitches, like the venerable Cherry MX series and its brethren and clones. They're mostly around 60-100g of force.
If you really want the feel of a computer mouse button, then you need to look at what they use, which is microswitches. But then you'll be entirely on your own as far as keycap design and illumination. These are also around 60-100g force.
Don't forget that the lighter the force, the more accidental button presses you have. And light/soft switches can be perceived as "mushy", rather than the decisive crispness of tact switches.
The other aspect you haven't mentioned is key
travel: how far the button moves when being pressed. Tact switches typically have 1mm travel or less. Mouse switches around 0.5mm (but the keycap is often a lever, so the actual travel varies). Keyboard switches are typically around 3mm. And other pushbuttons, like the ones for industrial control, are often 3-5mm.