We would say that your best bet is to go with wooden venetians, they come in a huge range of colours and give you that plantation shutter look, but without the bulk or price tag. They can be partly closed in the morning - giving you privacy but also giving you control over the light coming in. With larger slats you can angle the light towards the ceiling or towards the floor. We have a huge range of real wood (or faux wood) blinds to choose from: http://makemyblinds.co.uk/wooden-blinds.html  Also if it helps we have a handy guide on how to measure for a square bay like yours: http://makemyblinds.co.uk/blog/how-to-measure-for-a-bay-window/

Going with a roman blind would be a good choice, the soft fabric won't look out of place next to the curtain - https://www.makemyblinds.co.uk/roman-blinds/

How wide is the bay? (Not convinced the plan is entirely accurate if the previous people had a sofa on the left wall?). Ignore the furniture choice, was trying to find photos at the right angle! I might do something like this. You may also be able to have another chair on the left wall. If you go for an upholstered footstool you have more seating when needed and I’d choose a low back sofa so it’s not poking over the top of the window sill. If you don’t want the sofa to impose on the room too much, choose a colour that doesn’t contrast with the walls too much. Perhaps choose a rug that is large enough for all of the front feet of the furniture to sit on. You can always use masking tape to mark out the exact size of furniture.

There are numerous options, all with different costs and benefits. Here are some thoughts based on things I’ve done before. If your final finish is going to be wood panelling then stud work infilled with rockwool insulation or kingspan thermal insulation board (or similar) is probably the way to go. The insulation boards do have a foil backing and therefore resist water penetration fairly well. If there are damp issues then these should be resolved before insulating. Take the opportunity to sort out any pointing and then consider a treatment such as Bostik damp-proofer. If your final finish is going to be plaster then an insulated plasterboard is a good option. It’s not cheap but combines insulation, a moisture barrier and plasterboard. It’s also worth weighing up the cost and the time. Some of the cheaper options in terms of materials will be more labour intensive. Stud work and insulation is generally less expensive than insulated plasterboard but it takes longer to install.