The Sauder Beginnings Computer Desk or the ones from Desky should be good. The Sauder have ones that have 30 inches wide. The height is adjustable from 29.5 to 42.5 inches. They even have locking casters so it's more stable and doesn't wobble. Most of these are typically priced under $150 but price is going to vary so maybe take a look around on Facebook Marketplace or Best Buy. More on reddit.com

I use Husky work tables for my standing desks. They come with wheels. They have a model with drawers that is available in black or white. Here is a link to one of them. https://www.homedepot.com/p/Husky-52-in-W-x-24-in-D-Steel-2-Drawer-Adjustable-Height-Solid-Wood-Top-Workbench-Table-in-White-HOLT5202BJ2/311742117 More on reddit.com

I bought a Husky work bench from Home Depot. I got the bigger of the three models for $300. It has huge casters that allow it to be rolled around. I didn't install them and just use it as a sit/stand desk. The crank for raising/lowering the desk is manual. But it's not difficult to manipulate. The desktop is about 1.5 inch thick wood. I have a 32" and 24" monitor arm-mounted on the desk. I also have my laptop mounted on an arm. One arm is drilled through the desktop. The other is clamped. I've had this desk for 2 years and have no issues. More on reddit.com

Mine is on wheels for reasons very similar to your friend's. It is not wobbly at all, but it was also custom made with the intention of being on wheels. My assumption is that most desks are not supposed to be on wheels and would feel less stable when casters are added. One option you might consider is an adjustable height workbench (do a search at Home Depot for Husky adjustable height workbench). Those are rock solid and some of them are in dimensions very suitable for a desk. If I was to do mine again, I'd just buy one of those rather than going through the headache of custom making something. More on reddit.com