Hi! I've been tightlacing with corsets for a few years now, and all I can say is "beware!". Shopping for waist cinchers and 'proper' corsetry is an absolute minefield. Tonnes of sellers are currently latching on to the corset trend by claiming their naff lingerie will act as tightlacing or waist training corsets.
If you're serious about buying waist-shaping undergarments, then there is no substitute for a custom made underbust (the one in my profile pic was made by a company called Orchid, and fits like a dream despite giving me an 8 inch reduction). However, these cost an arm and a leg!
I always recommend Orchard Corsets for first timers, since these are amazing value for money, are shaped so much more nicely than a lot of steel boned corsets in the same price range, and offer a range of different silhouettes. Even seasoned corset snobs have been known to use them for long term wear. My partner is a trans woman, and she's been training with a level 3 underbust for months in order to make her lower ribs a little more tapered.
Happy shopping! X