What follows will be added-to as time allows.

Examine your Mini-14 carefully before purchasing, especially if purchased used.  It is quite common to see the lands of the muzzle-end of the barrel worn from improper cleaning technique and impliments.  Accuracy WILL suffer from worn muzzle rifling, depending on the degree of wear.  If the muzzle is not too badly worn, it can be re-crowned, thus restoring the very last bit of rifling.  If badly worn or nicked, the muzzle can be counterbored a bit, back to good, sharp rifling.  Every single Mini-owner should use a muzzle guide for the coated cleaning rod.  Brass tips, always.    

If your Mini must, for some reason, be sent back to the factory, do so before performing any mods whatsoever.  Ruger takes a dim view of non-factory alterations to their firearms.  There are reasons for this, but that is another topic.  The policy is longstanding.
That said, if sending the firearm back for factory servicing, consider ordering the "unobtainable", Ruger-only spare parts that you might want or need.  You will thus have factory-fitted "unobtainable" spares in the unlikely event your Ruger needs them.
Ruger's factory warranty service is very good.  They will fix, at minimal/no cost, problems that originate on their end.  OTOH, if someone has messed up their barrel through poor cleaning technique/impliments, that is not exactly Ruger's fault. The point is:  Have the factory perform any and all needed repairs, and buy any desired factory-only spares before embarking on any mods to your Mini.

To enhance accuracy, it pays to use the correct weight of bullet.  Ruger made Minis with a number of different Rate-Of-Twist (RoT) to their barrels..  The slow rates (like 1 turn in 10") are best suited to 55gn bullets, while the faster rates, such as 1-7", are better suited for heavier bullets.  Determine your Mini's RoT, and experiment with bullets in a weight range that it probably will like.

Ruger wooden stocks suffer from the flaws of all wooden stocks; they can warp due to humidity/rain, and added to these inherent flaws, they are often a loose fit.  Retrofitting a good, tight-fitting synthetic stock is an easy way to enhance accuracy.  You can always bed your wooden stock, using Brownell's Steel Glass bedding compound if you prefer the look of wood.  Use M-14 stock bedding guidlines, with appropriate modifications.

Some other inexpensive accuracy mods are adding an Accu-Strut, and adding some weight at the very end of the barrel, to reduce barrel whip.  I added a Choate flash suppressor (the short-barreled Mini really needs one), which also offers an improved GI-style blade with protective wings.  Adding a Scout rail, which clamps to the barrel in place of the original plastic handguard also adds some rigidity to the barrel.

Lots of Mini users have been baffled by the original rear sights, which, on the standard model, look like the rear sights on a Garand.  Unlike the 1MOA adjustments on the Garand's rear sight, the old standard sight was adjustable in 1.5 MOA increments.  Many users wound up chasing the zero because they did not understand this.  One can carefully file/dremel additional slots in both elevation and windage wheels on the Ruger, thus producing a rear sight that is adjustable in .75 MOA increments.

Synthetic stocks:  Some require stock liners, some don't.  If you see a pic of your prospective stock, and it has large screws in the sides of the stock alongside the receiver (like OEM wooden stocks), it requires a stock liner.  Almost certainly it will require a fore-end liner also, and the two interlock.  In many instances, both these parts need some minor fitting to syn stocks, as the wooden stocks' fit is loose enough to not require fitting.  I strongly suggest obtaining new parts (Liners, screws and lock washers) from Ruger first.  Reason for this is that to get the greatest possible increase in accuracy from your syn stock, you will need to grind/file/sand the stock liner to fit the new, tighter stock.  If you used the liner out of the wooden stock, it will fit the wooden stock even worse than before, as it will be slightly smaller.  IOW, every stock that requires one should have its' own, fitted, and permanently installed stock liner and fore-end liner.  One first fits the liner to the stock––removing any stock liner metal as required to obtain a tight fit to the stock––, and then files down the liner if there is any mis-fitting between the metal liner and the metal of the receiver legs.  Again, you want a tight fit, so easy does it here, also.  all this is straightforward, and you will be able to see where metal removal is needed.  NEVER remove any metal from the receiver itself, just the stock liner.
You want the stock liner to be a tight fit, so easy does it.  Both parts are inexpensively obtained from Ruger.   It is a real pits switching the barreled action between stocks unless you have addressed this issue.  since the stock liner and the fore-end liner interlock, it is a double PITA to switch out both parts.  Make life easy for yourself, and do it up right.
A little history: When I got my NIB stainless Mini back home,,I noticed removing and inserting mags took a fair amount of effort.  Reason was that there was a considerable mis-fit between stock liner and receiver leg, bending receiver leg inwards.  I removed enough metal to fix problem, and mag issue went away.