I won't recommend a specific printer (which is what you really ask for), but offer some comments that might help.
In general, the papers used for Laser and for Ink-Jet printers need to be quite different, so usually they are specified for which type of printer they suit. I worked in production of specialty coated fine papers so I'm familiar with these.
In a Laser printer the toner is dry and applied to the paper electrostatically, then heated with a blast of high heat to melt the adhesive on the tiny toner particles to bond them to the surface. So the paper must be able to stand up to that one-sided blast of heat without curling up. It also needs just the right electrical conductivity for the toner deposit part of the operation. An Ink Jet printer lays down quite a bit of water-based ink, so the paper needs a way to absorb that water without distorting, and then release it by evaporation afterwards. Ideally the process also should "separate" the coloured pigment or dye particles in the ink from the water, so that these particles are held very close to the surface where they can interact with light, while the water seeps down deeper into the surface before re-evaporating. There are no special requirements on electical conductivity for Ink Jet printers. Earlier Ink Jet papers required a particular class of pigment particles in the coating on the paper surface which was difficult to make, but more recent papers use different coating pigments that are easier at manufacturing time and not quite as good for the separation process. This also has meant that SOME papers can be made that do a reasonable job in both types of printer.
OP, your application adds more requirements. You are trying to print designs on a substrate that can then be affixed to another surface using an adhesive. Surely the simplest material to start with, as you say, is a labeling product that usually consists of a front "paper" (or other material) with a pre-applied adhesive on its back, and a protective backing sheet that can be peeled off and discarded. You should NOTE that the third product you linked to is NOT that - it is only the front sheet (in that case, Mylar) with no adhesive or backing. So you would need to find a way to stick it to something after printing. The other two both are synthetic polymer front sheets (polyester or vinyl), and both are specified for Laser printers. The major reason for that is that it really is not possible to make a polymer sheet with the capacity to absorb quickly, and then re-evaporate, all the water of an Ink Jet ink. On the other hand, one can make a polymer sheet that is able to tolerate the heat blast in the Laser, and also has a surface chemistry the works electrostatically and will accept the adhesive for bonding toner particles to the sheet. Additionally, the adhesive used on the back of the printed front sheet will be particularly suited to stand up to the heat blast in the Laser printer.
For both Ink Jet and Laser printers, sheets of labels often are the ones with multiple small labels laid out in a grid. When using them the most common cause of jamming in the printer is the EDGES of each label. Either the heat (Laser) or water (Ink Jet) in the printing process distorts the label material and can cause the edges to raise slightly. Then the curved path of the entire label sheet going around rollers causes the edges to rise even more, and they catch on nearby stationary items. But for the materials you propose to use, the front printable sheets all are entire sheets with edges only at the very periphery, where they are well bonded to the removable backing sheet. Plus, the total length of edges is much smaller than the total length of many edges on many small labels, so the probability of trouble is much lower. In many cases you would be producing a sticker which is smaller than the full sheet and of irregular shape, but the cutting (forming edges) is done AFTER the printer processes are finished.
Net result? For using the first two materials you linked to, many Laser printers will do the job well. Finding a printing material for use in Ink Jet printers will be more difficult and may require sheets with a paper single uncut front sheet, which is NOT transparent and may be less tear-resistant, depending on what the final use of the sticker is. On the other hand, if you do need a printing substrate with colour or white and opaque for some stickers, you probably can find such (whether paper front sheet or not) designed for Laser printer use.
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