My NGS result is in "fastq.gz" format. is there any recommendations of softwares or websites I could use to process the data and hence assemble the mitogenome?
Your question needs a bit more detail. What mitogenome are you assembling? How were your samples prepared, were they purified for mitochondrial DNA etc.?
Next it is important to determine what computational resources you are in possession of.
Ideally your pipeline would be as follow:
Unzip your sequences using gunzip, then performing quality filtering using FastQC, the FastX toolkit or prinseq.
If you have already done this, assembly can be done in any assembler. I have personally found SPAdes (http://bioinf.spbau.ru/spades) to work best.
More important than assembly will be to ensure all the assembled contigs are of mitochondrial origin. This can be done filtering against your organisms genome.
Alternatively you can do a reference based assembly using tools like bowtie.
See this paper for an example: DOI: 10.1111/1755-0998.12492
Hi--if you have a Mac you can download a simple mtDNA pipeline I wrote (it will also work on a PC through Konsole). It uses BWA and Samtools and creates a very simplified vcf. Everything you need is there--assuming you are aligning human ntDNA. Just be sure if you want to annotate the vcd files that you use the correct aa codon table. Let me know if you would like the link.
If you want to perform a assembly, firstly you need to check whether your reads are contaminated with adapters or not using fastqc. if so, remove the adapters using tools like cutadapt. if not, you can trim your sequences using sickle (it accepts gz file also, so do not need to unzip your files). Then you can assemble the data using SPAdes, megahit, CLC genomics workbench, velvet etc. So many choices. You can try one to several to find the best option.