Personally I would say try getting the following products one at a time and see how far you want to go. This isn’t the order that I would apply them to my face, I mean buy things in this order and then see if you want to add the next product or not.
1. Something for your overall complexion you have options here depending on how much coverage you want (ie how pigmented you need the product to be - more pigmentation covers up more flaws, although if you go to far it can end up looking cakey).
A. If you have fairly good skin you can get away with a tinted moisturiser or B.B. cream. My favourite is Urban Decay One and Done, which moisturises, provides some coverage and has SPF 20.
B. If you want something stronger, use a moisturiser followed by foundation. I just like using a basic own brand Superdrug moisturiser and Urban Decay Naked Skin Foundation.
NB. Whichever product you use, don’t forget to lightly add some to your neck too as otherwise your face can end up looking disconnected.
Another NB. If you find that the either tinted moisturiser/B.B. cream or foundation is not lasting well through the day or is going a bit orange after you wear it for a few hours, then add a setting powder on top. This will help keep everything in place and stop the product from reacting with oxygen in the air. My favourite is Charlotte Tilbury.
2. Mascara This can make a massive difference and open up your eyes. My favourite is Blinc tubing mascara because it’s totally waterproof and other brands used to leave me with smudgy eyes.
3. Something for the lips Use whatever lipstick or lip gloss you like. There are different types. Liquid lipsticks tend to stay on the longest but can dry out your lips. My current favourite is Kat Von D Studded Kiss lipstick in Lolita II. You can add lip liner if you want to help define the shape of your lips, but this is optional.
4. Blusher My favourite is Too Faced Sweethearts Perfect Flush Blush in There’s Something About Berry.
5. Concealer This is another complexion product. Use it under the eyes to hide dark circles and generally brighten up the skin there, and on any any blemishes, scars etc. My favourite products for this are by Charlotte Tilbury. She has an eye concealer which comes with a special under eye moisturiser, as well as a general concealer for other areas.
6. Eyeshadow Which colour you pick depends on what look you are going for. If you want to get fancy, you can apply more than one shade and blend them together (eg onecolour over the lid, a darker colour in the crease and lighter colour in the corner of your eye), but if you want to keep things simple just go for one colour over the eyelid. I would go for either maybe a light shimmer like Urban Decay’s Virgin to make the eyes stand out, or a more neutral shade of theirs like Laced.
NB. If you find the eyeshadow doesn’t stay on long enough (eg it migrates to the creases of your eyes) then use a primer before adding the eyeshadow. This is particularly likely to happen if you have oily skin. My favourite is the Urban Decay anti-aging one.
7. Something for your brows This could be higher up on the list depending on your brows are naturally like. A lot of aging women dye their hair but ignore their brows and it makes the hair dye more obvious if you know what I mean. There are various products you can use - pencils, powders and gels. I think pencils are tricky to get right and so would recommend starting with a coloured gel which will make them look fuller and keep the hairs in place (a bit like mascara does for eyelashes). My favourite brand is Anastasia Beverly Hills. That brand also does a good pair of small scissors which I use to trim them so that they are nice and neat.
I think those are the main products I would suggest for a minimal look. You will probably need to purchase some brushes to apply the products above too, although some people just use fingers. The RealTechniques ones which you can get from Boots and Superdrug are pretty good. I prefer to use an egg shaped sponge for applying foundation/B.B. creams because I find it easier to blend. You can get these everywhere nowadays and you just need to make sure that the sponge is damp so it doesn’t suck up all the product.
If you get into make-up there are further products you can explore like:
Primers - make foundation go on more smoothly.
Contour powders - used correctly, these can make your face look slimmer and more sculpted, you can even make your nose look thinner with practice.
Highlight - To add a glow to certain areas, often used on cheekbones.
Bronzer - to mimic the effect of a day in the sun.
Eyelash curlers - Not strictly a product but can be useful to help open up the eyes.
But these are nice but not minimal.