the thing that got me into handi rifles was of course the cost. I bought a really nice (to me) 7mm mag (winchester bolt-gun) a few years back. It shot fairly well, but had to have two trips to the local gunsmith to make it shoot really well. By the time I bought the gun, equipped it with a good scope, and made the above mentioned trips to the gunsmith, I had around $1500 tied up in the rifle. I carried it for one season and while I never banged it up I was at times more worried about banging up the gun than I was worried about hunting. Sure, it wasn't a $5000, one of a kind rifle, but to me the money tied up in the gun is substantial.
So, one day at a local gun shop I saw a handi rifle on the rack that was chambered in 270. $400 later I had the rifle and a pretty decent bushnell scope on top of it. It didn't shoot sub MOA groups off the rack, but neither did the above mentioned 7mm mag. The 7mm mag had to go see a gunsmith to shoot sub MOA. Well, to be fair, it didn't have to go to the gunsmith, I just didn't feel confident doing the work myself, so I chose to take it to the gunsmith. The 270 however did shoot well enough to drop every deer it has been fired at. I later bought a second handi rifle in 30-06 that has a kill for every round that has been fired through it (in hunting situations) as well. The 30-06 didn't shoot sub MOA out of the box either, but still shot well enough to drop its targets.
Now, a few years into having these two rifles I stumbled across this site, and starting with the 30-06 I went through an accurizing process using information found in the FAQ's, and the 30-06 is now shooting MOA (as of this morning...thanks to a snow day and not having to teach 8th graders!). The 30-06 has had a trigger job by me using the information in the FAQ for a grand total of about 50 cents, I floated the forend for about $3 worth of dremmel sanding pieces and an O-ring, and a little bit of bedding work that required about $10 worth of materials. So, for under $15 above the cost of the rifle, and a few hours of time (I'm slow), I have a 30-06 that shoots 99% (and I'll say i'm the 1% error) as well as my 7mm mag that was over 3 times as expensive.
I'm beginning the same process on the 270 now and expect it will get similar results. It may even shoot a little better than the 30-06 being my second run through on accurizing a handi rifle.
Now I just need pay day to get here so I can get a handi rifle coming that is chambered in 35 whelen. That will more than cover the biggest critters I will ever get to hunt in my lifetime. I may in time pick up a 4th handi in a smaller caliber in case I ever get to do any varmint popping, but I haven't done any thus far in my life and don't foresee any in the near future.
The barrel accessory program has great pricing, but I probably won't ever take advantage of the pricing because I don't think it would work out well swapping barrels after the bedding work, etc. I should probably check with other members here on that, but in my head it seems as if it would be problematic. However, when the whole gun is $250, I don't feel too bad about buying them complete for each caliber.
That's about all I can offer for why i'm hooked on the handis.