After collecting your information, what I understand is you want to get contamination free+ good quantity DNA using conventional protocols. After that you are going to amplify and perform capillary sequencing.
0. If you sample is bacteria, check for the mix culture or pure culture or not
1. To isolate bacterial gDNA, lysis part should be done very well.... using fresh lysis buffer solution or may be you can use small sterile bead to rupture the cell wall.
2. The remaining protocols can be followed using phenol:chloroform:isoamyl alcohol (25:24:1) steps.
3. PCR amplification step should be precise there should be single band.
4. PCR clean up has to be performed
5. During the capillary sequencing PCR step, company recommended protocols has to be followed. Sequencing PCR product should be in kept in dark by rapping with AL foil...
6. Capillary tube has to check properly before you proceed sequencing.
If this is a PCR product sequence, then the problem is not with the quality of bacterial DNA. If you got a PCR product then the bacterial DNA was fine. (And very simple colony boils work fine as PCR templates.) It seems more like there is some problem with the purity of the PCR product used for sequencing or with the choice of primer for the sequencing reaction. There is a great simple PEG precipitation method for purifying PCR products for sequencing at:http://methdb.univ-perp.fr/cgrunau/methods/PEG_precip.html
But you should also be aware that it is generally not advisable to use the same oligonucleotide primers for fluorescent Sanger sequencing that you used for PCR primers when preparing the amplicon to sequence. That may actually be the problem with the Sanger sequencing result that you have shown.