Look at Remy as an exception to that rule of thumb, while Giroud hasn't done bad (although he's nothing special for me) Lacazette is a very good player and a top young talent, but wouldn't be suited to a team that plays 1 up top like we do. He'd be better at Liverpool or Arsenal, as much as I hate to say that.
Gamiero was on fire a few years ago, but hasn't set either the French or Spanich leagues alite since. He's a decent impact sub, but I reckon if we're looking at anyone from abroad as our 1st choice striker (writhin our price range) it should be Carlos Bacca. £9mil. Buy-out clause and would suit RM's system to a tee. Him and Batshuayi (the 'gamble') would be decent I think, although I'd prefer Rom or Bony but both seem unrealistic at this point.