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Which forecasting model should I start with?

Start simple, beat the baseline, then add complexity only where it earns its keep.

Before any model: plot the series, forecast it with naive and seasonal-naive methods, and set up a rolling-origin backtest. Every model below has to beat those baselines on it.
What are you forecasting?
One series, or a handful
Does it have a repeating seasonal pattern?
Yes, one season (e.g. yearly in monthly data)
Use
Exponential smoothing (Holt–Winters) or SARIMA

Both model trend and one season well; fit both and keep the one that wins the backtest. Damp the trend for long horizons.

Yes, several at once (e.g. daily and weekly in hourly data)
Use
Regression with Fourier terms, or gradient boosting on lag and calendar features

Classical seasonal models assume one season of fixed length; Fourier terms and calendar features handle several.

No clear season
Is there a trend?
Yes
Use
Damped-trend exponential smoothing, or ARIMA with differencing

Trends rarely continue unchanged; damping keeps long forecasts sensible.

No
Use
Simple exponential smoothing or a low-order ARIMA

A level that moves slowly is all there is to model — anything more will fit noise.

Hundreds or more related series (products, stores, sensors)
Use
A global model across all series: gradient boosting on lag features, or N-BEATS / DeepAR with long histories

Learning across series beats fitting each alone once there are many; deep models pay off with many long, related histories.

A series driven by known factors (price, weather, promotions)
Use
Regression with ARIMA errors, or gradient boosting with those factors as features

Uses the drivers directly — but only if their future values are known or forecastable at prediction time.

How much a price will move, not where it goes
Use
GARCH-type volatility model

Returns are close to unpredictable; their size clusters and can be forecast.

When something changes or goes wrong
Use
Changepoint or anomaly detection

A different question from forecasting: finding breaks and outliers rather than predicting values.

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