I would probably go for the back boards as 150mm x 19 or 22mm and the front battens 50mm x 19 or 22mm. This will give approximately 120mm back board showing, allowing for a 10mm gap between the boards.
Allow for ventilation between your boards and the brick wall, to help longevity of both, you could install a Tyvek type breathable membrane on the battens.
As for what timber to use, if you go for cheaper softwood, then it’ll be tanalised or pressure treated, which is fine but it’s generally fast growth stuff and will need regular maintenance/painting.
How about Douglas Fir, Larch or Western Red Cedar? You may find a local sawmill with some and these varieties can be left as they are and will silver off as they age. Their natural resins make them very resilient. Alternatively, a something a little more left field could be green Sweet Chestnut.
Ideally, the wider boards want to be quarter or rift sawn, although that tends to be expensive due to waste, so just make sure you lay the boards with the heart outward facing, I.e. the growth rings are convex to the wall.
HTH