I'm struggling to find a matching blue colour for this red one I've got:
By 'matching' I mean similar feel, in terms of brightness, contrast, lighting etc...
I'm new to graphic design so I don't really know how to find similar colours.
There's (luckily) not one answer for your question. The simplest solution is to take the RGB-value difference from 255. In your case red (255-207=48), green (255-58=197), blue (255-27=228). In HEX: #30C5E4.
I prepared different solutions for you here.
For the first one I only changed the hue value (+180°).
The second one is the solution from my first paragraph. If you look at the HSL values it adds +180° to hue plus it also mirrors the lightness value. 50% lightness is the center, so 46% lightness from your red mirrors to 54% of the blue.
The third one mirrors the saturation value as well.
The fourth adds +180° to the pHSL model value.
The fifth also mirrors lightness of pHSL (my favorite).
Bonus: since you mentioned brightness and contrast: take any of the blue colors and match the (relative) luminance [Lum] value of your red = 47%...
Which one you choose is then up to your specific requirements and personal taste...
There are some "rules" regarding color harmonies that you will find very helpful for this case and any future ones you might have regarding colors.
Colors that are opposite each other on the color wheel are considered to be complementary colors (example: red and green). The high contrast of complementary colors creates a vibrant look especially when used at full saturation.
Analogous color schemes use colors that are next to each other on the color wheel. They usually match well and create serene and comfortable designs. Analogous color schemes are often found in nature and are harmonious and pleasing to the eye.
A triadic color scheme uses colors that are evenly spaced around the color wheel. Triadic color harmonies tend to be quite vibrant, even if you use pale or unsaturated versions of your hues.
The split-complementary color scheme is a variation of the complementary color scheme. In addition to the base color, it uses the two colors adjacent to its complement. This color scheme has the same strong visual contrast as the complementary color scheme, but has less tension.
The rectangle or tetradic color scheme uses four colors arranged into two complementary pairs. This rich color scheme offers plenty of possibilities for variation. The tetradic color scheme works best if you let one color be dominant.
You can use an online service like Kuler to calculate these.