Ask a Bowman Thread.

I started my Marksman the day Ludi was released back in 2006, and back then, there was no such thing as STRless or even low STR. So mine is capped at 100, with 40 more from equips so I can equip my Reverse Black Beauty. Anyway, it's all according to preference/how much money you have. But for the most part, you want to have 120 STR to equip the level 120 weapons, be it all from equips or AP. Generally, it is more expensive to go completely STRless because equips that are godly scrolled for STR are stupidly pricey. Just remember one thing: Your STR must always be equal to your level to equip your weapons.

Here's how I see it:

STRless = No strength, obviously. Keep your STR the same as when you rolled your character.
Low STR = Between 50 and 60 STR. Get 60-70 STR from equips (Like I said; freaking expensive)
Regular STR = Cap at 100 and get 20+ more from equips (Cheap, and honestly, your damage will not be that different if you decide to do this)

There really isn't a "right" way, just so long as you don't have an absurd amount of STR, and obviously pump the rest into DEX. 100 is a bit high, but that's what I did because that was my build back in the day. I can't really afford to reset them out yet, so I'll just have to deal with it until I get better STR equips and NX to reset some. If you want my advice, don't go completely STRless. Go low STR. It's not terribly hard or expensive, and you end up with a little more DEX in the higher levels, which is never a bad thing. But ultimately this is your choice.