Help! New house and no idea what to do with space at the back

[IbizaLovesSundays]

My DH and I have just moved into our first home together and we have a small space out the back. I have hopefully attached photos. We won't be in the house more than 2 years, so don't want to spend thousands but I would like to make it look a little bit more 'cared for'. We have removed a lot of the ivy as can be seen in pictures and it does extend to the left and the right a little at the bottom of the path (currently raised bed on left and gravel space on right)
Does anyone have any suggestions as to how I could transform or spruce up this space for about £500?

Congratulations! Is the blue gate at the bottom the boundary?

What's the building behind it with the blue door!

What direction does the garden face? Light looks to be a bit of an issue.

I can only think of tidying it up as you're doing and perhaps painting the fence a light colour. Seagrass or pale grey. I've never actually painted a fence so I don't know how to prevent colour leaking through to your neighbour's side. Hopefully someone can advise!

In the same vein I'd consider painting the brick outbuildings white/ pale grey to smarten them up and provide a backdrop for foliage. I have no idea whether this is a ridiculous idea - it would depend on the surrounding houses/ buildings

I might take inspiration from the blue gate and have 3 tall blue glazed planters dotted either side of the gravel path to draw your eye up towards the wider part of the garden, space permitting. Have two on the sunny side and put something lush and shade-loving like a fatsia japonica in the one by the outbuilding. At least you can take them with you when you move

Is there space for a table and chairs/bistro set at the end by the gate?

Keep on top of the weeds and top the gravel up on the path if it needs a refresh.

Here's an example of a tiny space. They've crammed it full of plants which you might not want to do (some would take a year or two to establish). I like the defined colours and textures.
here

Those Pinintrest ideas are the way to go. Old brickwork is beautiful and the patina of time cannot be replicated, so I wouldn't paint it. If I was the next owner/ tenant I d be really upset and try to remove paint.
Work out the aspect and what will grow. You will have shady bits and lots of interesting plants grow in shade.
It's nearly the time for garden centres to be clearing their plants for winter, as they don't like overwintering them, so you should get some bargains. Go for some height with climbers that have all year interest, such as winter jasmine.
Spend some of the money on interesting containers, that you can take with you and maybe a small, water recycling water feature.
It all looks fun, enjoy the garden.

I assume that as you're only there 2 years that you are renting ie you won't be able to paint the brickwork or make permanent changes?

Oh sorry I totally misread, apologies if you're renting and I've offered a load of duff advice!

Stick with the interesting planting and don't paint anything without permission from LL

We are renting but we can do whatever we want with the property (except knock through walls and knock down outhouses lol)
The blue door is the boundary yes- and the taller blue door behind it is part of the primary school that our alley (behind the blue door) backs on to. The garden is north facing.