This is the million dollar question.. There are hundred's of thread's similar to this.
Your first choice will be your realm. Now technically and statistically Syrtis is the best realm for archers, Ignis second and Alsius last. BUT!! This alone should be your only reason for choosing your realm. There are many many different factors. I'll assume that you'll be playing Horus; so (I'm sure people will agree that) Ignis is the strongest realm, Syrtis has the most numbers and Alsius is the smaller of the three. I wont go into more detail, but PM if you do want more.
Next you'll choose your race. This will have a direct influence on your starting stats. For example in Ignis; Esquelio's have 5 less Dex (Dexterity) ([25] an archers main stat - add's damage) but they have 5 more Int (Intelligence) [25] and Const (Constitution) [25] - which means more mana and hp; than the other race available for archers in Ignis; Molok's. So it's a trade off - Damage vs. Health / mana. In Syrtis the situation is similar. You have Half Elves with start with 30 Dex, 25 Const and 20 Int, and Wood Elves with start with 30 Dex, 20 Const and 25 Int. This means that Half Elves have slightly more hp, but slightly mess mana, whereas Wood Elves has less hp but more mana.
I'm not going to tell you which is best - As there is no wrong answer. Then once you've chosen your desired race, you'll have 5 extra stat points to distribute. I would reccomend putting them in a stat that suits your race. For example, if you chose an Esquelio, you might want to put your 5 points into Dex as they start with 5 less than Molok's, but on the other hand, you may want to boost their hp / mana further if so put your points into const / mana respectively. Now, I wont tell you what is best - as there is no right or wrong answer, this will have to be up to you. However, I will offer you this advice; don't put your 5 points into Concentration (Conc.) This stat only creases your hit chance slightly, spell focus slightly and your critical hit chance. In other games these might be very important things, but you do not have to worry about them in Regnum Online; A) Because Hit chance only semi works, B) Spell focus is an unknown value and C) As an archer you'll be doing plently of crit's anyway.
Lastly will be your class choice. Once you reach level 10 you'll need to choose between a Marksman or Hunter. Now this I can only help a little with. Both classes are very, very different and provide much different gameplay.
A hunter is a scout unit that can tame pets to help them fight. They have (argueably) decent defense and again (argueably) decent damage. They can use Camoflague to hide from enemies and can track their prey too. They have low to medium range (20-25m*) and are the fastest class in the game. Hunters are best suited to lone, or group hunter and are not nearly as good at forts compared to Marksmen, but this is a general opinion and not solid fact.
Marksmen on the other hand are easily twice as powerful. They possess much greater range (25-~40m**) and similar defense, however they have unparalled ranged defense. They are slower than Hunters, but are still capable of good speed. They are best suited for fort wars where they can kill targets from range, while being fed mana from their conjurer's.
If you use the search feature of the forum's you'll find thousands of threads which ask the question "Which is better, Hunter or Marks?"
*This is not a class based range, but a fixed bow range. Hunters tend to use short bows which are range 20 - 25m.
**Marks tend to use Long bows which are range 25 - 30m. However they posses a range passive which increases their range.
Both classes have a spell which temporarily increase their range, but is only useable for Long bows, so is more often used by marks.
Here are some useful links:
CHARACTER CREATION GUIDE.
REGNUM ONLINE WIKI.
BUILD SIMULATOR.
If you need mroe help, PM me.