A good lab scale with the precision he stated should be just fine. There is no reason to prefer a dedicated reloading scale, other than the inconvenience of doing the units conversion.
Stuck cases are hard to get out. Sometimes you can drop a cleaning rod down the muzzle and just give it a little whack. Often it's a lot harder than that, and really not something you want to risk.
A serviceable reloading setup isn't that expensive. You can pick up a used Lee press for around $40, or their hand press (will help you develop upper body strength, maybe not the best solution) for around $50, including a tube of lube. I think the price of pair of Lee RGB dies is around $22 [one to full length form the case and one to seat the bullet], and a shell holder is about $4. Of course, you need case lube. I use RCBS Case Lube 2, put a few drops on a folded paper towel, and use a Q tip to lube the inside of the neck. A Lee Perfect Powder measure is under $25 and will speed up the process quite a bit. Digital calipers that are more than adequate are available from Harbor Freight for around $16 if you watch the sales. Before you use the brass a third or fourth time, you'll want the Lee case trimmer that works in your drill. All together, that might be $12 for all the pieces. The most important thing to get is a good reloading manual. I don't know if Hornady still puts out their economy paperback manual, but it used to be around $12. It has reload info for just a few popular cartridges, but I'm pretty sure that 223 is among them, and that's all you need.
I started out with a Lee Loader for my bolt action 30-06. The only equipment I had was that plus a little balance scale, and I made decent ammo. You can make good ammo with very basic equipment, and it will work for you, but I worry that you're going to have less success using a Lee Loader for a semi-auto.