The Normal Route is the easiest, safest and fastest on account of the cable car and chairlift system. However, good acclimatisation and fitness can be had by eschewing these in favour of a trudge up from the valley (recommended). Not the most majestic of mountains, Elbrus will impress more for its size than anything else. Nonetheless, the views outwards to the south and the watershed of the Caucasus and the Bezingi Wall are very impressive and reward enough for any long hard trudges on this great beast of a hill.
Note: Elbrus, much more than high peaks in the Alps, appears prone to parties - especially those that are guided - using ski/walking poles instead of ice axes on its apparently steadier sections. This is a mistake. A week before the moderator for this page was on Elbrus, a party of seven Russians with a guide slid off an essentially horizontal traverse on the south face. What had appeared relatively steady terrain then proved otherwise. As their slide steepened their lack of ice axes or having ice axes to hand prevented them from effecting what would almost certainly have been a very simple ice axe arrest. All seven, including the guide, plunged into a crevasse and died. An absolutely needless occurance. As technically straightforward as Elbrus is, ensure an ice axe is carried - regardless of other, usually guided parties, not doing so.