Lots of good advice here. I won't reiterate it all and instead leave it to, "*points up* what they said."
With that said, now, there are some definite finer points of storm chasing that would likely help you. The first is not to be ashamed of being nervous about being in a harmful spot. Fear leads to caution, which keeps you safe. I was pretty timid in my first several years of chasing, too. To be honest, what got me over most of it was dipping my toe in a little more each time and coming out unscathed, but also having a few experiences where I clearly goofed and paid the price. Since then I have known where the line is. You will (or already have) discover your own personal comfort line in a similar fashion.
Next, think of storms in a relative sense rather than in cardinal directions. While others have said it is safe to be southeast of the storm, that assumes typical Ely or NEly storm motions. There are many situations in which storms do not move in those directions, and thus your specific positioning on a storm should change accordingly. I think what Jeff H. and Dean said speaks to the idea that a desirable position to be in is
both "ahead of" and "off to the right" of the storm's path. Find the storm motion vector and then sweep a path along that whose width is determined by the reflectivity edges of the geometric union of the FFD and RFDs.
First priority - stay out of that swept area. Keep in mind that if a storm is moving southeast (as I believe the Sharon Springs, KS storm last year was), this safe spot is actually to the southwest or even west of the storm. East or southeast puts you directly in the path of the core, so it is not surprising you took a hit.
The object is to
stay in visibly clear air (but also outside of significant hail or wind), and I have found that you can generally see though 40 dBZ precip as long as it isn't several miles thick. So you can afford to be in an area around the edge of the FFD with reflectivity values roughly 40 dBZ and below. Many chasers will haphazardly charge into visibly obscured conditions to catch a rain-wrapped tornado, or just punch through a core to see what is behind it. Most of the time they get through just fine (although luck is involved with that, and hydroplaning is an understated hazard). Sometimes, however, like with Silver Lining Tours last year, they get
one of these (NSFW quip) greeting them on the other side, which is a good PSA for not plowing into an area when you can't see.
As far as staying out of "not obvious big hail" and strong non-tornadic winds, don't forget about the
vault region of a supercell (the area immediately downshear of the updraft...which often appears visibly clear...giant sporadic hail stones don't obscure visibility like densely packed and small rain drops do), and read radar velocity. Outside of the RFD, strong surface winds are pretty rare, but if you see a big downburst/downdraft signature on radar (learn how to diagnose those), then stay away from the area unless you are prepared to take it on. Also, learn how to
identify an RFD signature visually - the "cut" in an updraft base (which gives it a horseshoe appearance) or a small-scale shelf cloud are usually strong indicators of the leading edge of an RFD, so assume the surface RFD boundary is slightly out ahead of that. Winds within the RFD can be pretty nasty, either with or without falling precipitation, and this may not always appear on radar velocity. But check radar velocity always, and stay out of the RFD altogether if you cannot confirm low wind speeds within or are unwilling to take damage from what might be lurking in there.
A good sign of safe RFD transect is if you can see clearly under the base and there are no imminent signs of cloud base rotation or dust flying up from the ground.
