Saladin, it did not take much work on my #1B in 25-06 to get it to shoot beyond my wildest expectations.  When I bought it, the barrel was tight on one side of the barrel channel and accuracy was poor. All I had to do was relieve that side of the barrel channel.  I left one spot of contact at the very front of the forend.   I didn't do anything else - no trigger work, speed hammer, etc.  

Here is an example of how it shoots:   Last Saturday I took it to the range to check out the point of impact at 200 and 300 yards.  At 200 yards 4 shots fired off sandbags went into a 0.91" triangle (first and last were overlapping)  At 300 yards, I fired the first two shots off sandbags.  They made overlapping holes!   I then took it off the sandbags and fired two shots from a hunting type field position.  Those two shots were less than 2" apart at 300 yards. 

The Alex Henry forend should not present a problem accuracy-wise as long as you don't try to use a sling for shooting.  That barrel band sling swivel is best used for just carrying the rifle, not shooting.   

You should be able to load the 7x57 up to it's full potential in the #1.

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Very few of the #1's are really inaccurate.  The biggest issue is getting the barrel/forend/frame interaction right.  Some are good out of the box.  But most respond to a bit of tweaking.  There are several ways to do it all of which are well within in the skill range of anyone who has handloaded ammo and none require complex or expensive tools.  Information is readily available on line, from this site and others as to how to go about it.  Best course probably is to start with factory ammo to get a baseline, tune the action/forend/bedding then start handloading for accuracy.  if you try developing handloads first or at the same time as adjusting the forend you'll have too many variables.  you might also try shooting it with factory ammo off the sandbags without the forend--resting on the bare barrel ahead of the spring hanger.

tweaking the action itself to get faster locktime and better trigger pull is another area of improvement you can pursue at a later date if you feel it is needed.  again there is info here to help you

Welcome to the ASSRA forums

I've experienced both ends of the spectrum.  Had a 458 Win Mag that was very accurate.  Also one in 22-250 that was good.  However, a #3 in .22 Hornet was pathetic.  Couldn't consistently hit a 9" pie plate at 100 yards in calm conditions.  No amount of tweaking this and that made any difference.  Overall, I would have to agree with what has been posted.  They are generally accurate rifles.  

The .22 Hornet I think was a problem from the earliest days.  I remember an article in a Gun Digest from back in the 70's that chronicled the adventures of a gentleman trying to get a #3 to shoot in that caliber.  He was not very successful in the end either as I recall.  

Good luck to you.  Let us know what you end up with and how it shoots.
Marc

Marco, I suspect that that #3 in 22H was a cascade of bad stuff happening.  Unfortunately the 22H while a fine little small game hunting round is not known for steller accuracy without considerable work with bullets and load development.  Then of all the #1 variations I suspect that in the short barrelled lightweight #3 would be the hardest to shoot well with the combination of short light stock and the usual Ruger single shot bedding issues. Even the 45-70 version, while a superlative little brush gun for hunting was not much of a target rifle.
 I had a #1 in .30-'06 that was incredibley accurate.  I now have a well tuned #3 action rebarrelled with a heavy short barrel in 38-55 that is my ASSRA competition bench gun.  It's fairly new to me but I suspect that with another season or two of learning what it likes the biggest factor keeping me in the muddle-of-the-pack will be my skills or the lack thereof.
I also have a #1 that SteveD is working on that should turn out to be another good one when done.

Ed Cooksey has a very very fine little modified #3 that Steve and he did that shoots very well indeed.  I may be wrong but I think it's in the dell/miller cartridge.  In the last issue there is a pic of it on page 37.

Hopefully sometime early next year we will be doing an article, maybe two specifically on the Rugers that have been showing up at Etna Green.  There have been some really innovative things done to some of them but all of them are capable or great accuracy or they simply would not be there

Yes, for an accurate .22H, you need a Martini...
users.pandora.be/Gert.Claes1/BSA22H16-10-2005.jpg

Ditto to what DWS said about #3's and Hornets.  I have a #3 in 45-70, and it is pretty obvious that it isn't a suitable rifle for benchrest in the original configuration, LOL!  

I also have a Low Wall in 22 Hornet, and factory ammo had a shotgun pattern.  Careful handloading utilizing a neck sizing die got it shooting teeny tiny groups though.  

I don't think anything is inherently wrong with the #3 action.  Mine has a great trigger and I believe I can build a very accurate rifle on it.  But not with the factory stock!

I've already proven to myself that there is nothing wrong with the #1 action...

I just laugh when I read about the trials and tribulations bolt action shooters go through trying to fix action bedding problems and such.    

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I have a #3 Ruger, rechambered from Hornet to .221 Fireball with custom wood that shoots VERY well with both jacketed and cast bullets.

I also have a #3 in .45/70 that is my next project to work with. I keep the board posted. It'll be shot entirely with cast bullets.

Dale53