After the Senate split into different factions, the Jedi were no longer welcomed everywhere across the Republic. In the Imperial systems the Jedi were shunned and made unwelcome by the leaders. Their offers to help were rejected and they asked to leave the systems. But this was nothing compared to the persecution they suffered in the Separatist systems. The Separatists were openly hostile to the Jedi. They were threatened, abused and in extreme cases bounties were taken out on them. By the time the Clone War started, the only places the Jedi were welcome were in the Republican systems and the few remaining neutral systems (these systems either had neither the urge or ability to get involved in Galactic politics).

At the outbreak of war, the Republican faction was the largest, but with the weakest military. Many of the individual systems had no military at all. And the military, in most of the systems that did have one, was small and defensive. They had very few warships capable of interstellar travel and the majority of their armed forces were part-time soldiers or star-pilots. The one thing they had to their advantage was the Jedi knights.
The Separatist systems, though not as many as the Republicans had a much stronger military. Most had permanent armed forces and were able to field deep space vessels capable of either space combat or planetary assault. But they weren't a unified force. There was no overall commander, and hence, no overall strategy. Each system deployed their forces with little or no co-ordination with their neighbouring systems, let alone the faction as a whole.
The faction with the strongest forces was the smallest, the Imperials. They had been preparing for just such an eventuality, it was after all their whole philosophy. They had a unified force, large warships, able to transport both soldiers and fighters. These ships could engage in combat, bombard or blockade planets, and then had the forces to launch an invasion. They had a supreme commander and had been planing and practicing for a war against the Separatists for a long time.

With the declaration of was came the need for the Senate to appoint a war leader, as the current leader was, by their own admission, not a soldier or general, and incapable of conducting any sort of campaign. Since the withdrawal of the Separatists from the Senate, the Republicans had the numbers to control the voting, so they had the choice as to who would hold the power during the war. While there were several potential leaders amongst the Imperials, the Republicans didn't trust them to relinquish control once the war was over. And, if they were going to choose one of their own Senators, they had to be one that the Imperials would follow. The Imperials pushed for their candidates, but the Republicans eventually installed one of their own. He was a retired general who had fought several successful campaigns, and was trusted by both the Republicans and the Imperials.

Next: The Clone Wars (Part 2)