Everyone thought Voldemort was dead until Philosophers Stone, and even then no one really believed Harry.
Still no-one believed he was back when the death eaters attacked the Quidditch World Cup in Goblet of Fire or when Harry told everyone he was back following
Cedric Diggory's murder.
It wasn't until the events in the Ministry of Magic during the Order of the Phoenix that Voldemort's return was taken seriously by the Ministry.
Until this point there would be no help from the Aurors. Tie into this the fact that the Ministry seems to be compromised, by people such as Dolores Umbridge.
Eventually the Ministry falls to Voldemort during Deathly Hallows after this the Ministry would not be any help.
The Order of the Phoenix was re-established following events in The Goblet of Fire when at least Dumbledore and Sirius Black took Voldemort's return seriously.
No one knew about the Horcruxes until Half Blood Prince
Harry: "So if all of his Horcruxes are destroyed, Voldemort could be killed?"
Dumbledore: "Yes, I think so. Without his Horcruxes, Voldemort will be a mortal man with a maimed and diminished soul."
Dumbledore probably had an inkling about Horcruxes following the events of Chamber of Secrets.
- 1 year between the event's at the end of Goblet of Fire and the fight between TOotP and Voldemort's Death Eaters, where TOotP were dealt a big blow and weakened.
- Another 1 year between The Order of the Phoenix and The Half Blood Prince during which the existence of Horcruxes is confirmed and TOotP is dealt another, even bigger blow.
- Then 1 more year before all the Horcruxes are destroyed and Voldemort killed. At the cost of a lot of TOotP
So during the 3 years that the existence of Voldemort is known/accepted
- Most of the first 2 years the Horcruxes are not known about and are therefore not in play.
- They are dealing with Voldemort directly as you suggest and 2 of the strongest wizards in TOotP are killed.
- Once the Horcruxes are known about and have to be destroyed, no loss of life for TOotP is caused whilst trying to get and destroy any of them
unless you count Dumbledore's suicide by Snape following contamination by the locket.
- And in the third year a large number of strong wizards within TOotP are killed, in direct conflict with Voldemort and his Death Eaters.
This shows that for 2/3rds of the fight with Voldemort the only plan would be dealing with Voldemort directly as the Horcruxes are not known about.
The high death toll to TOotP also suggests that the plan of killing Voldemort is far riskier than going after the Horcruxes and with Horcruxes still in play, if Voldemort comes back before they can all be destroyed, there will be far less wizards of power left to resist him.
Following changes to the question I have added the following timeline of events in an attempt to answer the questions assumption that it would be easier to kill Voldemort before destroying the Horcruxes.
24th June 1995 - Voldemort regains his body, Harry escapes and tells the world. Cornelius Fudge refuses to believe this is the case. Dumbledore reinstates the Order of the Phoenix
17th & 18th June 1996 - Battle at the Ministry of Magic between The Order of the Phoenix and Death Eaters,
the death of Sirius Black,
and the Ministry officially recognise the return of Voldemort. However by this point many in the Ministry including numerous Aurors are already on the Dark Lord's side.
20th April 1997 - Harry Potter using Felix Felicis gains the memory of Tom Riddle and Professor Slughorn discussing Horcruxes.
22nd April 1997 - Harry and Dumbledore view the memory and discover that Voldemort has multiple Horcruxes.
The hunt for the Horcruxes then begins
30th June 1997
Severus Snape kills Dumbledore - NOT Horcrux Hunt related
27th July 1997 - The battle of the Seven Potters
Mad-Eye Moody dies - NOT Horcrux Hunt related
1st August 1997 - Voldemort takes control of the Ministry of Magic
28th December 1997 - Salazar Slytherin's locket destroyed
Dobby dies - NOT Horcrux Hunt related
2nd May 1998 - The Battle of Hogwarts
- Helga Hufflepuff's Cup destroyed
- Rowena Ravenclaw's Diadem destroyed
- Nagini Destroyed
- Voldemort's Soul in Harry Destroyed
Severus Snape, Fred Weasley, Nymphadora Tonks and Remus Lupin all killed - All NOT Horcrux Hunt related (also 50 unnamed fallen wizards)
This gives a total of 0 deaths due to the Horcrux hunt against 8 named and pretty powerful wizards (including, arguably the most powerful of them all), plus 50 others all due to direct conflicts with Voldemort or his Death Eaters.
For 1 year and 9 months of Voldemort being back the Horcruxes were not known about, the only thing the Order of the Phoenix could do was battle Voldemort directly during this time. The Order was the strongest it would ever be during this time and it failed to kill Voldemort.
For the last 11 months the Horcruxes were known about. They were all destroyed during this time.
Hunting Horcruxes sure looks like the easier option to me.