1. You said that you are extracting your 'genes'. If you isolate genomic DNA and use it as the template for PCR amplification for your gene, then purify the PCR product using a kit (such as PCR purification kit), then use the purified product for sequencing (NGS).
2. If your DNA quality is low, your sequencing results will not be good, and many unreadable bases will be expected. Use a good kit is recommend.
Its important to know the purity of genomic DNA if you are using gDNA as your sequencing template. if the purity is good enough then you can proceed for NGS. The only problem with conventional Phenol/Chloroform or Chloroform is that tere may exist residual phenol contamination or some salts after ethanol wash steps. In that case i will suggest you to use a Kit based protocol.
if you are using PCR amplicon of you target gene then its important to perform a cleanup of PCR amplicon as already told by Yuan or Gel purification of PCR product. There are many ways and kits are available for it .
The most important factors is your template for sequencing whether its NGS or Sanger, You need to have a good quality of template and with optimum concentration