What you see on your image should look very similar once printed and I'm not certain what makes you anxious about it. I think it will print out well even without any special effect.
If you want the colors to be vibrant, you can use a coated paper. An uncoated paper will absorb the ink more but in general it does it equally and you don't lose a lot of contrast. It's still less "shinny" and more dull than a coated paper though.
There's also types of stock that already have some subtle pearl and glitter effect. Since the ink is not opaque, the effect of the paper is shines through the ink and everything looks a bit glittery. Unfortunately I can't remember the name of that stock. You should go see a printer and ask for different types of glittery stocks, they will certainly show it to you.
The design can be printed in full color process (CMYK) or hexachrome or spot colors (pantones) but if you want more details for your light, I suggest you choose CMYK or hexachrome. Printing with only Pantones kind of flatten all the colors to the same level and will look more dull.
There's also selective varnish that can be used but in general, you can't use gradients with that kind of effect; it's a solid. It could be an option to have a matte varnish on the background part of the design and/or a lustrous one for the artwork part. You can use both or only one, it depends on how much contrast you want to give to the glossy effect. For example, if you want a subtle effect, you can use a glossy varnish only on the lineart and have all this printed on a coated paper. There's also different types of varnish and techniques; aqueous ones are less "solid" and thinner, more subtle. UV varnishes are thicker and have more dimension, they're a bit "embossed". And then if you have the budget, you can laminate the cover with a matte plastic and have a UV varnish applied on top of it! It gives a nice satin effect to your print and add some dimension to the parts that are glossy.It's beautiful but very expensive to produce because it requires a lot of precision (and material).
Finally, you could always consider using a metallic ink for some parts of your illustration. Metallic inks are not really metallic like a foil effect but they do have a nice shine and are semi-opaque; they could be applied only on the portion of your artwork that have some light reflection. In fact, I think it would probably be a good technique to use for your design, there's also different color options in metallic inks.
What I suggest you do is to go meet a printer, show your design and ask for printed samples of their previous projects. You will see with your eyes what can be
done and it should be easier for you to figure out what technique to
use. The printer will also be thrilled to help you because they
usually love being able to print special projects like yours and
combining their techniques in different ways, according to your
Make sure to select a quality printer; these techniques above can look very bad if the inks or varnishes are not well aligned! Some techniques are maybe too expensive to be used on big runs and are usually reserved for high class products where the cost-per-print is not an issue.