Im sure there are threads like this, sorry for the clutter. First off let me say that I'm fairly new to the ar world, and I have recently purched a 10.5 inch pistol from Head down products. And let me say that this thing is sweet. But I need to throw a sight on it.( going crazy seeing that thing with no optics) so I'm asking yall. I don't wanna spend over 500 dollars so keep that in mind please. Also, if you can tell me why you prefer an optic that'd be great. I'm not the type to go and buy with ought knowing as much as I possibly can.

Thank you all and hope to interact more often on here.

Welcome to the board.  There are lots of knowledgeable guys on here that can provide good feedback on any topic.  I should know - I'm relatively new to the board as well.  ;)
I'm sure many will chime in but it might help for you to provide some additional detail on your optic needs.
Is this going to be more a range gun (toy), home defense, truck gun, hunting?
What distance would you like to shoot out to accurately?
Is weight a concern?  
Red dot vs. magnified scope - preference?
Going to want a magnifier if choosing a red dot?  
Are you going to have back up iron sights?
Etc.
I'm sure there are other questions that answering I haven't thought of at the moment to assist people in their responses.
But supplying some of this additional info will help generate more responses I'm sure.
Best,
Jim

https://www.primaryarms.com/Red_Dot_Sights_Primary_Arms_s/903.htm

Cheap ($) and made in China. Primary is a great company though.

Burris Fast Fire III with AR mount isn't bad if you're looking for quality under $500, just small.

You can also pick up an Eotech 512 for $350-75, or certain display/blemish models for $475ish.

Aimpoint PRO has a great battery life and is within your budget.

Is this going to be more a range gun (toy), home defense, truck gun, hunting? Range toy.
What distance would you like to shoot out to accurately? 50yrds accurately
Is weight a concern? No, weight is not a concern.
Red dot vs. magnified scope - preference? red dot (is there a red not with a small magnification 2x maybe?)
Going to want a magnifier if choosing a red dot?
Are you going to have back up iron sights? Will have backup sights.
Etc.

You should also research RTS type sights. They are off-set 45 degrees and are low-pro. Search Amazon they are about $30-250 bucks.
To employ sight system cant rifle to 45 degrees (to the left, yea.. right hand only at this time) so the sights are over the bore and engage target.  

That way you can put on any optic and be able to use both.

Can you hold out til Black Friday? You'll have more options at your pricepoint and save some cash

yea I do not absolutely need to find the right optic right now just itching to get one on, so i may wait it out. and can someone explain If i should need, or want a magnifier. and what is the best magnifier and any more info on them is welcomed. just trying to learn

Buying a magnifier for a red dot isn't a cheap addition and adds more weight. I could see this perhaps on a rifle, but not a pistol...then again it's only my opinion.  

Are you going to shoulder the pistol while firing? If so, a Weaver V3 is a nice clear scope and let's you vary from 1-3X. I have a couple on rifle setups and like the light weight and that it's a one piece unit. It has a duplex crosshair and doesn't meet your red dot desire though. You can easily find them under $200.