The Russian army was huge and that was its main problem in terms of modernising ALL of it. You could certainly have modernised elements of it quicker, but the most obvious were also the most traditional, ie the guard units.
Being huge, logistics were again huge. There's no point getting a small army to your border with Germany or Austria-Hungary (arguably it would be OK to the Ottoman border) so yoou have to set up systems to get ALL of them there. This is why Russian mobilisation was so tricky - they couldn't PARTLY mobilise, they had to complete it.
As things stood, the Russians certainly matched the Austrians as equals, and in 1914 at the height of their mobilisation could arguably have beaten the Germans in the August 1914 campaigns and forced them back onto West Prussia.
Time was not kind to the Russians, the longer the war went on, the greater their problems became.
IMHO Russia's best chance to come out of the war victorious is for it to end earlier. Alternatively, the Ottomans remaining neutral would have had great butterflies in its wake and not only opened up the Black Sea supply route (and kept open the trade route) but probably have led to some sort of Southern alliance against the Austrians.
The earlier the peace comes, the less harsh the terms are going to be on the losers. A 1914 victorious peace would probably bring reparations from Germany and Austria, and the destruction of some border fortresses. A 1916 victorious peace would bring larger territorial adjustments, including something for Poland that pulls at least some territory from Austria and Germany.
Best regards
Grey Wolf