What’s the best filler or treatment (no laser/Botox) for the start of fine barcode lines?

Hello, and thank you for your question. The right dermal filler may be able to give you the smoother look you want by filling in the vertical lines around your lips. Other options include professional skin care products such as a topical retinoid that can help to boost collagen production. I would suggest sitting down with a board-certified cosmetic surgeon to explain your goals and create a treatment plan that’s right for you.
 

The vertical lines between the nose and lip margin and those of the lower lip and chin, are related to the contraction of the circular muscle around the lips that has taken place for many years in the background of sundamage and / or smoking.
Botox can help significantly reduce the contraction but only in those people who don't have an elongated lip and have lost their appearance of the upper teeth when smiling. The number of units used is very small and I also don't tend to inject Botox in musicians who play wind instruments, and those whose oral communication is critical for their employment such as singers and journalists,etc.
Fillers often are used for these wrinkles, such as Juvederm, Restylane, Volbella, and Belotero.
Laser resurfacing with the fractional carbon dioxide laser (Fraxel REpair), Halo hybrid laser, Sciton Contour and Profractional lasers, and Infini microndeedling with radiofrequency can help improve these lines, but as the muscle will still contract, the lines will never go away 100%.
The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice.  The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs. 

hello, I would suggest a filler like Belotero or Volbella to address fine lines around the mouth. The cost will vary based on geographical region you aware located, but likely $600-800 per 1 cc syringe.