For your budget, I would suggest you to go for Razer DeathAdder Essential Wired Mouse. This is one of the best mouse for sketchup under budget of 40$. You will surely love this mouse.
Here are main features of this mouse:
If you use macros, I would suggest using any of the razer naga series.
You can program the most basic tools/commands on the side keypad and it will save you A LOT of hand movements over the keyboard.
(I have del, esc, tab, ctrl, shift, L (line), R(rectangle), C(circle) plus a few macros for plugins plus 3 shortcuts for different curic pie menus. That way you can have almost zero toolbars on your GUI.
Also, the scroll wheel can zoom in/out with increments if you push it left/right instead of scrolling.
Edit: I just saw the budget. these mice are at the 100$ range but still I would suggest saving some money to improve your productivity (and thus make up for the extra cost with the money you will earn 
)
To tag onto what @arisleme said, and get a little philosophical, you may want to save up a little extra before you buy your mouse.
I know that there are plenty of people out there that love their $12 mice and I have no problem with that. I look at the things I use on a daily basis and my mouse has to be a tool I use more than anything else. Many modelers use a mouse more than they use a keyboard, but most keyboard cost significantly more than their mouse counterparts. I often smile when I see someone spend upwards of $3k on a computer, but want to save money in their main input device.
I’m not lecturing here and have a habit of doing things “on the cheap” when I can, myself… but when it come to my mouse, I generally do spend more knowing that I want it to perform and I want it to last.
End of rant!
I have several cheap mice, but then I use a stylus most of the time.
I find the lags are from the mouse battery being depleted.
I would totally need out seeing a video of your setup. More please!