Most of them are covered in that other thread, though it is specific to my skin needs but not labelled by ingredient so I've listed below plus some alternatives. Apologies, these things always turn into a novel since I'm not all that happy giving universal advice/recommendations purely on the back of my personal experience, especially considering my very specific skin likes and dislikes.
Vit A- I use Verso that has the unique Retinol 8 patent which is supposedly 8 times more effective than standard OTC Retinol and especially suited for sensitive skin. I think it's great (shea butter based though so not for everyone) but wouldn't be able to tell you if it's 8x better. I will be trying the Ordinary 2% Retinol simply for the possibility of being able to spend significantly less on the facial serum but there is little that will pry me away from the Verso Retinol Eye Serum as it's bloody brilliant and surprisingly affordable for the amount you get (30ml as opposed to the standard 15ml) and lasts forever.
I'm not really an advocate for eye creams unless, like me, you're especially sensitive to other products in that area or want to target it specifically with a proven active with an appropriate formulation (Retin-A and strong acids should not be used in that area as skin is generally too delicate, some can use Retin-A in the area but really should be done under supervision of a medical practitioner). Alternative retinols to consider are by The Ordinary (2%), Paula's Choice, and SkinCeuticals (1%). Sunday Riley's Luna Oil gets very mixed reviews, Pestle & Mortar's retinoil is also worth considering though relatively new. Pay no mind to the percentages though, they indicate very little. You have to take in consideration pH followed by some difficult maths to understand the effective % of actives on the skin (unlike Retin-A where the percentage is indicative of actual strength as required by law with all prescription medication).
Vit C- I use a Japanese one currently (Melano CC) that is effective but % unknown unfortunately cheap though. I've used Kiehl's Powerful Strength Line Reducing Concentrate at 10.5% in the past which is a good gentle daily option to get started with (the higher concentrations really more of interest to those with sun damage and PIH) but I wasn't a fan of the use of silicones in it (gives false indication of the condition of your skin, masks a lot of unknowns). I'll be trying one of The Ordinary's one next. The gold standard is Skinceuticals Ferulic C+E that has a patent on the best pH for the formulation and a price to match. NuFountain c20+Ferulic is a good alternative price wise (from amazon.com?tag=mumsnet&ascsubtag=mnforum-21 not uk) with a very similar formulation and is made fresh to order. The Ordinary's one is bargainous and initial reviews appear positive. All these are L-AA based, the Vit C form with the most scientific backing but is unfortunately very difficult to stabilise (it's recommended to keep most in the fridge to delay oxidation).
Vit E- as mentioned is usually high in something (currently my Rice Bran Oil) and one can easily purchase Vit E oil for v. little if desired. It's just not much of a star ingredient as the others but it's a solid hard worker.
Niacinamide- it's in both Verso's formulations (though % unknown) and at a high concentration in my Naruko Magnolia Gelly, the entire Naruko Magnolia line (from Taiwan) is high in Niacinamide 3-5%. Alternatives are Cerave PM lotion (4-5%), or the Ordinary Niacinamide 10% + Zinc to use either buffered in as a booster or on its own. The Olay products are rumoured to hold high % of niacinamide but I don't know if they've ever published them.
AHA- Biologique Recherche Lotion P50(W), there's a reason people love this and it has a cult following. 'Fetus skin in a bottle' is not too far off of a description. There's many other glycolic based alternatives but I tend not to get on with them well. Pixi glow tonic at an ineffective pH for any proper exfoliation brought me very close to the brink of rosacea (never had it before or after) after only a few uses with a careful approach, for others it's a miracle worker. Alpha-H Liquid Gold is an alternative as are the Nip+Fab (all glycolic). Clarins (Gentle Exfoliator Brightening Toner) and the Ordinary do Lactic Acid versions.
BHA- Paula's Choice 2% BHA Liquid, there's very little that comes close in all honesty. I have the travel size as I don't need to use it all that often. COSRX BHA Blackhead Power Liquid from Korea is a decent alternative albeit much gentler and less strong (also 2% but it uses a different form of BHA).
Hyaluronic Acid- Kohaku Hada Lotion from Japan because it's cheap, you get quite a lot (220ml vs. 30ml) and unlike Hada Labo is paraben free (they're not as dangerous as the internet likes to think, I just happen to not get on with them well, among many other types of preservatives). The Japanese lotions (somewhat in between a serum/toner in consistency) are formulated well with not just any old hyaluronic acid in it. They're also the original pioneers of HA. The premium version from HL is a godsend to very dry/dehydrated types but may be too rich for some. Hyalamide is an alternative or the NIOD version if you want some added anti-ageing ingredient in there with it. Supposedly the Kohaku Hada Lotion has anti-ageing amber extracts in it, there's no science to back that up.
SPF- Japanese all the way. They're formulated to the highest standards with extreme cosmetic elegance and the newest and most effective UV filters. Ideal for year round use rather than the occasional holiday. I use Kose Sekkisei Sun Protection Essence Milk but it's quite an expensive one (due to added beneficial ingredients, but also my specific needs). The Biore UV Aqua Rich Watery Essence Sunscreen is the #1 seller in Japan for a reason and a firm favourite under western users too (wouldn't recommend for a sun destination holiday though, it's an 'indoor sunscreen', not sweat and water resistant). French pharmacy ones like LRP Anthelios or Bioderma are good seconds and better suited for outdoor use, especially as they boast higher PPD (UVA protection as opposed to UVB which relates to the SPF number) ratings but break me out like nobody's business.