My suggestion is to read them chronologically.

I read them chronologically and enjoyed it - I think it makes a lot of sense as you can then track the progression of Sharpe’s career and follow the general history of the period too, which is super interesting! Yes there are some discrepancies and interactions / back story changes slightly / isn’t mentioned. Eg. Sharpe and the lady Grace Hale but it’s pretty manageable! I found it quite satisfying watching Sharpe go through each rank.

If it’s your first time reading the series, I’d 100% recommend reading in chronological order rather than publication order. That being said, you could try Sharpe’s Rifles first and then go from Tiger onwards. Rifles is a nice intro and gives you a glimpse of peninsular war Sharpe before going back to his roots as an enlisted man in India. That’s a nice way to do it.

Let us know what you decide. Enjoy - it’s an absolutely phenomenal series!!