Photo credit for above idea http://www.hauthaus.com/

It looks like an enclosed verandah, or some kind of sunroom extension, is that right? What is your climate, it sounds as if heat is a concern but cold is not? What is the floor, if you were to build walls what would they be sitting on? The most budget friendly efficient solution to heat and light is external shading, but you also say the existing windows are unsafe, so presumably you want to replace them anyway?

Thanks for your responses! I will work on getting some of those things together (plan with dimensions, photos etc). Yes, it is an old external patio from what we understand. It has a concrete floor which isn't level - it is lower (to varying degrees) than the wooden floorboards in the rest of the house. We are yet to decide what to do with our floors so currently just have carpet taped over the concrete so our kids can play on it. We are in Brisbane, so have a sub-tropical climate. Certainly cold is a consideration as we find with all the glass we lose a lot of heat in winter, but heat is more of an issue.
We do need to replace the windows, or at least the bottom panels, because they are old and therefore not to code and not safe for our children. Some of the aluminium frames are corroding (we live near the water) and the windows really date the place, so ideally if we're getting the bottom panels replaced we would do the whole lot at once. I will post again when I have the other things you need. Thanks again!

Hi again! Please find extra info as requested. As mentioned above, climate is sub tropical (very hot and humid in summer, mild winters). Thanks in advance for any thoughts.

luckily the external cladding should be easy to match or you could use plain modern "fibro" wall cladding so my suggestions would be to enclose the original front verandah with stud walls up to at least 50cm (lie your wish photo) -75cm off the floor (to block out views of the street, allow wall space for bookshelves and toys use and use louvre windows to create much better ventilation (bottom of standard sliding, awning or casement windows would need to be higher to be safe without louvres) but you need to change the front entry so that the door can open inwards .. bug screened louvres windows are ideal for this location and i would also plan for external shutters on the eastern side of the living area to screen the morning sun, reduce overheating and increase privacy

Thank you @oklouise! I think you have commented on many of my questions over the years and your advice us always top notch and so helpful! So do you think we could get away with standard glass (e.g. no low e coating etc) with this aspect (especially as it may take a few years for the budget to extend to external shading)? We will investigate external shutters, we would need something really non-obtrusive as we have a beautiful Jacaranda tree out the front which makes for a lovely view. But we are really not loving having so much old glass around with small kiddies, so the windows are first priority.

it would be a crime to spoil your lovely view but i still think that modern louvres above a low solid wall would be the best choice at the front and side of the original verandah and external screens to shade the eastern side of the living area...the problem with budget is that it will never be cheaper than doing it properly the first time ..the glassed in verandah wasn't the best option and now you're having to replace it...thinking about a range of budget options for safety, sun and heat control ...consider the DIY stick on window films for all the windows ...a range of window films are available at the major hardware stores including one for increasing strength of glass, reducing heat transfer and frosted ones to improve privacy but you could also add plastic garden lattice screens horizontally inside the lower windows.. that should give some extra protection to the kids and can be recycled into the garden when no longer needed

Thank you @oklouise! Some great budget ideas there, should we need them - I hadn't thought of any of these! Next stop for us: quotes for external awnings/blinds and for a low solid wall. Thanks again!