The good news is a cottage garden is the cheapest style to have. Its also the easiest to get free plants for.
Are you on freecycle and preloved? They're a good source of cottage plants. You could place a wanted advert. Lots of cottage plants can be easily grown from seed and theres much pleasure in that. Ebay is another good source as are lidl/aldi /b &m. Some packs of seeds are 29p
Bulbs are cheap in b & m too. I also buy up the reduced to clear potted bulbs from supermarkets and diy sheds often for around 10p when the flowers are just starting to turn - at least you know the bulbs are good, the size of them when grown. Its something to look forwards too next year. Sometimes they get a bit of a second wind and other buds open once they're planted in the free space of the garden.
I'm doing my garden on a budget. Its nice in many ways to be forced to do things slowly, to watch your garden grow.
We have a 99p store near by. I brought 5 bare rooted roses last month and several honeysuckles, they're all doing really well. I also brought two packs of three hosta roots and i've got four good plants out of them, two are very week.
Our local Homebase tends to reduce plants on a Wednesday am. A big investment I've made was for two topiary yew pyramids £10 each (from £50). I also purchased a standard ball topiary privet for £6. Not bad for a 6ft evergreen to add some structure to my beds.
Now I start adding all this up its not quite so on a budget. But the costs are spread out. Its very much a few pounds here and there.
Regarding your lawn have you checked out offcuts on ebay and the possibility of laying it yourself. If you can be a little flexible on size there are sometimes big bits of fairly nice quality stuff. Have you got a rough idea of the dimensions?
A basic starter greenhouse is £10 for a four tier plastic covered metal framed shelf job. It would stand against the house and get you started at propagating and growing from seed for a year or two. Redoing the whole garden is a big project so maybe focusing on one or two element for this first year is the way forward. The cheap 2 ltr plastic fizzy drinks bottles make great cloches. You just chop off the bottom and bury them a little into the ground over your vulnerable plant, minus the lid for ventilation. Great for young tomato plants and keeping slugs off your lettuce.
If the shed is still functional put it on future years list. This year use pots/ growbags for veg and maybe focus on salad crops. Just start with a few tomatoes, a cucumber and cut and come again lettuce. You can still get grow bags for 99p and no doubt could fit four or more on that little patio area at the end of the garden. The grow bags will make a good soil contribution for your veg beds when they happen.
If the path is functional and its your main route in/ out it would seam practical to keep it. Have you thought about painting sections of it with any odds of gloss paint you have?
You could have hopscotch, kids hand/ foot prints - I'm sure pinterest has lots of ideas. Even snakes and ladders/ draughts etc. the DC could paint pebbles to be the draughts pieces.
Another low cost thing to start that will save you money long term and reap rewards is a compost heap. Sometimes local councils do really heavily subsidised compost bins. Ours used to do them for £11.
In the bed next to the decking is that a striking red robin? They're meant to be quite easy to propagate and make nice colourful evergreen border shrubs see RHS website for taking softwood cuttings to propagate. If you take twice the number of cuttings you want for yourself theres always the possibility of doing plant swaps at some point in the future.
On the subject of propagation have you thought about asking family/ friends if you can take small cuttings from anything/ everything you like in their gardens? Most people throw away bin loads of prunings that you could be converting into new plants.
Pinterest is great for creating a wish list of ideas. Lots of people post great budget ideas like raised beds made of old tyres. Cheaper and in many ways more practical than making from decking boards.