Getting SRA reads
SRA Toolkit tools directly operate on SRA runs. Toolkit has capacity to find requested runs at NCBI and download (and cache) only the part you really need. For example quality scores represent a majority of data volume and you may not need them if you dump fasta only (versus fastq). Or if you are looking at particular gene you may not need the reads aligned to other regions or not aligned at all.
If you plan to run data analysis in environment where getting data from NCBI at run time is unfeasible you can use SRA Toolkit prefetch utility to cache all data in advance. Read more at SRA Knowledge Base on how to download SRA data using command line utilities.
Please use SRA Run Selector to filter and download list of SRA runs in the scope of experiment, sample or study.