There are some pretty good HSS sets on the market, try to stick with well known branded types e.g. Dormer, Presto, Guhring for your more precision drilling needs as the more generic 'Chinese' imports tend to drill oversize. I have various makes of drills from various sources inc. boot sales, some were good some not so good. I am in the process of making up a set of drills specifically for brass, i.e. slip / diamond stone the cutting edge back so the drill doesn't snatch on break through, which can leave you with a broken drill in the piece you don't want a broken drill in . A set of 'Jobbers' drills will serve you well for normal bench drilling. If you need larger sizes get your self a couple of Blacksmiths drills, these have the shank machined down to fit the standard 13 mm chuck & tend to be shorter in length for strength. I have a couple on hand… 16 / 20 / 22 mm.
There are of course taper shank drills to fit your tailstock, MT1 – 3 is the usual for tailstocks we hobbyists have but of course this depends on the machine you have, yours may have tailstock capability of MT4 -5. I also buy small sizes in packs of 10 from the likes of… http://www.ukdrills.com/hss-drills/ ( usual discl. ) … which are very reasonably priced so if ( when ) I break one I simply throw it away. I am fortunate that I still have reasonable eyesight ( with vari focal / bi focal glasses 
that I can hand regrind most drills down to a size of 3mm, & on a good day 2mm with the aid of a loupe & gauge, another thing to check is eccentricity, roll the drill on a surface / glass plate & see what the tip does, you'll be surprised! I was using an extended centre drill yesterday & noticed an amazing wobble when it was in the drill chuck, I rolled it on my granite plate & the amount of run out was surprising for a ground centre drill.
George.