The cost is low if you know where or what to look for.
3 piece safety razor
1) Edwin Jagger 89L (mild to slight aggressive) £20-£21.50.
2) Muhle R89 (Mild to slight aggressie) £24.99
3) Merkur 34HD (mild to slight aggressive) £30.
4) or search old Gillette safety razor ... Safety Razor UK got some but price has gone up since. Adjustable ones are better to play with.
Anyone of the above should be a good start. Actually the head might be manufactured by the same company.
Badger brush (I did not kill any badger so don't blame me)
Spend around £15 - £25 for a badger brush.
This one
Any of these
Or just get some from departmental store ... Kent B4 is around £20 - £26
Shaving soap/stick (anything more than £5 is very very expensive)
No need to spend a fortune as the highly recommended one cost 44p to £3 that will last you a long time especially the shaving soap stick.
1) Palmolive shaving soap stick (highly recommended 49p - Made in Germany - from Superdrug at 69p or Wilkinson at 48p).
2) Erasmic Shave soap stick (very good 89p ... but I prefer Palmolive ... not sure somewhere now since my local stores stopped stocking them)
3) Akro shaving soap stick (very good £2.42 ... just because they are from Turkey still prefer Palmolive - get it from Shaving.ie)
4) Palmolive shaving soap tube £1.68 (very good)
5) Ingram shaving soap tube £1.68(very good)
6) Erasmic shaving soap tube (very good but not sure the price but less than £3)
Double edge or safety razor blade
The following brands are good so you might want to buy a sample pack of different brands before settling down on the one(s) you like.
1) Feather (sharp as sumurai sword ... Japan Made )
2) Iridium Super Blades (Russian made)
3) Gillette 7 O Clock Sharp Edge DE Blades (Russian made same factory as Iridium)
4) Personna Platinum
5) Any of the Gillette blades should be fine.
In fact most blades are okay .. apart from ...
Avoid the following blades as they got mixed reviews.
Merkur, sharp, Dorco, Supermax, Blue bird (some said ok), Laser ...
Check out here for sample blades.
Shaving.ie
Connaught Shaving
Oh ... a bowl or a coffee cup for soap and brush to stir in.
You can get most of the stuff from these online shops.
The gentlemans-shop
From Ireland
Shaving-shack
Connaught Shaving
Safety Razor UK
Traditional shaving
So there you go and I guess £45 - £50 should set you up nicely to last for a while.