Cleanse, tone, moisturise and SPF are the basics. If you're not someone who needs a lot of moisture then you could look for an SPF that doubles as both in the morning and just use a moisturiser at night.
I think a gentle exfoliating toner would work well for you based on your description. It would brighten the skin and might help with pores a bit.
Glow Recipe Watermelon PHA/AHA toner is really good, enjoyable to use and very gentle. It has a bit of viscosity to it so you don't need cotton pads - just pour a bit in your hands and pat over your face. It's not cheap but you can often get it on offer (bound to be some Black Friday offers) and the full size does last a while.
I also rate MediK8 Press and Glow toner for the same reasons. This is a thinner formula and does require cotton pads to use. Again not cheap but often discounted and lasts a while.
If those are both too expensive I've read that Pixi Glow tonic is a good budget dupe for the above. Currently on offer at Boots for £12 for 200ml. I've not tried this one yet though.
For daily SPFs the Beauty of Joseon SPF is highly rated and very affordable to use regularly. Superdrug stock some of the range now and possibly you'd like some of their other products also.
Byoma is another brand that is well priced and can be bought at Boots. Their cleanser is also supposed to be nice. They have different ranges for different skin types.
In addition to the above whilst it's not strictly skincare I'd consider trying a primer under your foundation products. e.l.f do a good pore blurring primer that is inexpensive. You might find it helps your make up sit better than before and last a bit longer.