Code 39 and Code 128 are the most stable linear barcodes for damage and distortion.
The most compact barcode is Code 128 (both numeric and symbol data).

Recommendations for 1D barcode creation and further reading:

• Create 1D barcodes with cell size (single-wide bar) at least 2 pixels.
• Use the padding for 1D barcodes with size not less than 4 cell size.
• The more barcode height, the more reading quality.
• Use optional checksum for barcodes without default checksum (Code 39, Interleaved 2of5, Standard 2of5). This will help you to avoid mistakes in barcodes recognition from images with low quality.

2D barcodes

Data Matrix is the most stable 2D barcode for damage and distortion. Also it is the most compact one. After come Aztec, QR, DotCode and PDF417.
All 2D barcodes can contain text and binary data and can restore up to 30% of damaged data using Reed-Solomon error correction algorithm.

Recommendations for 2D barcode creation and further reading:

• Create Aztec, DotCode, QR Code and Data Matrix barcodes with cell size at least 3 pixels.
• Create PDF417 barcode with cell size at least 2 pixels.
• Use the padding for QR Code and PDF417 barcodes with size not less than 2 cell size.
• Use the padding for Data Matrix barcode with size not less than 4 cell size.
• Use the padding for DotCode barcode with size not less than 3 cell size.
• Use the padding for Aztec barcode with size not less than 1 cell size.