Iron sights are "okay", aperture sights better, low power scope (if your eyes are wearing out like mine) are best.
Trigger pull is subjective and varies from frame to frame. Currently I have two 30/30s, a 357 Max, a 45LC and two 22 Sportsters... all the triggers are different. The trigger in the frame with the 357 max has been "tweaked" (see FAQs for trigger tweaking info), and so has one of the Sportsters. Those two have awesome triggers. The others are quite acceptable and I don't plan to spend any time tweaking them. And none of them has needed any forend "tweaking".
Accuracy on all of mine is perfectly acceptable for hunting. And as of yesterday, since I took all the centerfires to the range yesterday, the 357 Max appears to be the most accurate (with some 180 gr handloads) and the two 30/30s are neck-and-neck with factory Federal 150 gr Power Shok rounds. The 45LC was bordering on disappointing, but I only had a bit of ammo to try, so I am not giving up on it quite yet.
I might point out, that yesterday's shooting was done with a WGRS aperture sight on the NEF (modern) 30/30 and the Topper was wearing an old Weaver 3x scope - and the group sizes were so close to identical that I didn't bother measuring. So I guess it is theoretically possible that the 1995 NEF with a scope might shoot tighter groups than the old 1972 Topper... I dunno, and truthfully I don't care... The Topper weighs in about 1 lb lighter than the NEF and it is the Topper I plan to be packing around in the field this fall, and I am willing to accept hunting accuracy from it.
I've had several 30/30s Handis and Toppers over a 25 yr period and all of them have had from acceptable to excellent accuracy without tweaking and with factory or hand loads. And I don't recall anyone on this forum ever complaining about the accuracy of a 30/30 - someone may have, but I don't recall it.
So my experience suggests that "tweaking" a Handi trigger (whatever the caliber), and/or the forend (as wcf3030 says) can help accuracy, rolling your own handloads can do the same; and even if you do nothing but take it out of the box and clean the manufacturing gunk out of it, a 30/30 is very likely going give acceptable accuracy ... and the potential for amazing accuracy lives in the "tweaking" and ammo.
Cheers
Kerry