The Angela Marchmont and Freddy Pilkington-Soames books are loosely connected but it doesn’t much matter which series you start with.
The Freddy books published to date can be read in any order without affecting your enjoyment or introducing spoilers.
The same is true of the first eight Angela books, but I recommend leaving books 9 and 10 (The Scandal at 23 Mount Street and The Shadow at Greystone Chase) until last and reading those two in strict order, as they form a two-part story, followed by the short story Angela’s Christmas Adventure, which follows on from books 9 and 10 and contains spoilers. The other short stories can be read whenever you like as they are self-contained with no spoilers.
Angela Marchmont Mysteries
The Riddle at Gipsy’s Mile Book 4
The Incident at Fives Castle Book 5
The Problem at Two Tithes Book 7
The Trouble at Wakeley Court Book 8
The Shadow at Greystone Chase Book 10
Angela's Christmas Adventure Short Story
The Man on the Train Short Story
A Question of Hats Short Story
Angela Marchmont Mysteries Vol. 1 Books 1-3
Angela Marchmont Mysteries Vol. 2 Books 4-6
Freddy Pilkington-Soames Adventures
A Case of Murder in Mayfair Book 2
The Lucases of Lucas Lodge A Novella