what sizes?
All home sewing machines have used the needle system 130/705H (same as 15x1H or HAx1) in the last 40+ years, so the only thing you need to decide on is size of the needle and point type needed. (Don’t get serger needles with designations like ELx1 or DBx2 — they won’t work in your machine correctly!).
Needle size is determined by the fabric — you want the smallest hole poked in your fabric possible, but if the needle size is too small, you get skipped stitches. FWIW, a size 80/12 needle will sew almost any garment fabric if you only want to get one needle size.
Needle point style is determined by the construction of the fabric: is it woven, is it knit, how closely woven or knit. Schmetz has a light ballpoint needle suitable for most wovens and most knits called a "Universal". Again, if you don’t sew much, and you sew both wovens and knits, a Universal needle will probably do what you need — though other point styles may do a slightly better job.
More: http://www.schmetzneedles.com/pdf/new_Needle ABC_GB_S.pdf
There are a lot of good needle manufacturers out there — Schmetz is the most commonly found one; others include Groz-Beckert, Lammertz, Klasse, Organ. I’m not sure who’s making Singer’s needles now.