Alright, enough horsing around for me --- people have given you pretty good options to choose from; just a rehash:
VSonic GR07 --- one of the best all-rounders you can buy, at any price. They are right at the edge of your budget, at $155 from LendMeUrEars, and perhaps less from some eBay sellers, but they are well worth the price. They're neutral, non-fatiguing, and very technically sound. The sound improves with burn-in to minimize its biggest 'flaw' which is sibilance, and the ergonomics are excellent. They have fast bass that is punchy whenever needed, but never bloaty.
Hifiman RE262 --- also at the tip of the spear at $150, but like the GR07, should be a true keeper with (from all accounts) great mid-centric sound. I've designated this to be my very next IEM... The impedance at 150 ohms means that it'll need an amplifier to perform at its best though, and if you don't have one, you may want to hold off on this guy till later.
Hifiman RE0/ZERO --- the darling of the Hifiman line, for bringing top-tier SQ at a sub-$100 price point. Their analytical nature is ultra-detailed, and treble should be amazing, but you may be underwhelmed by their lack of bass. The RE-ZERO is a little more 'fun' than the RE0, but it has a strange balanced plug that requires an awkward adapter for a normal TRS input.
Shure SE215 --- a little more affordable, but feels more like a FOTM than true super performer; I didn't get a very long time with her, about 30 seconds --- she sounded good, and had great ergonomics. A good, safe choice, from a famous, reputable brand. It's mid-centric and has great bass response.
Westone UM1 --- Westone always has a great fit, and will sound good, but the UM1 is aging; there are comparable products at a better price point, like the... (see below)
MEElectronics A151 --- haven't listened to them, but have heard nothing but good things about MEElec's stuff. The SR armature inside seems to be a good price/performance type of driver.
MEElectronics C51 --- heard great things about these ceramic-enclosed IEMs too
Phonak Audeo PFE121 --- haven't heard these either, should be very good though
Fischer Audio DBA-02 --- beginners might not be able to appreciate these IEMs, sort of like how they may not know why a RE0 sounds so good; it's truly an excellent IEM though, and I use it everyday alongside my GR07. The bass is ultra-tight, but can be punchy with the right source, and the treble is some of the most elite treble there is. It's effortless in the top end. However, it does cost a little more than $150 and is very hard to find ready-stocked stores online.
UE Triple.Fi 10 --- if you can manage to find them discounted at under $150, they're a true value. They sound excellent (if a little mid-recessed) but they have terrible fit, so try to find a pair to try on first.
Sunrise Excape/Excited/Impressive/yadda yaddda yadda --- I don't know much about them, but yeah, they come highly recommended.
There are many others... too many to count... you really need to look at Joker's thread as well as ClieOS' threads... they provide invaluable resources for beginners in search for an IEM that fully suits their tastes and preferences.