You didn't mention which Swiss Army Knife you've been using, but your reference to "tiny blades" leads me to believe you're used to a fairly small knife. I'd suggest you start with something that's not a whole lot bigger than you're used to, or carrying it may be too much of a drag. It comes in WAY under budget, but I'd suggest the Byrd Meadowlark 2 FRN with serrations.
View attachment 681303
It's got a pocket friendly size and weight that will be a good transition from a SAK to a modern folder. It will also get your feet wet with "hole opening" to determine if a Spyderco might be in your future. The 8Cr13MoV steel is decent and easy to maintain and the bi-directional FRN handles provide a very effective grip. The back lock is simple and easy to operate. Best of all, you can buy 1 with your budget and bank about $30 to put toward the "next" knife as you get a little grounded as to what you like or don't like.
The Kershaw Link is a decent choice as it can be found within your budget, I'm just not a fan of assisted open knives. It's probably significantly larger and heavier than what you're used to also.
I'd avoid anything by Gerber and although the SOG Twitch has a following, I'm not a huge fan of most SOG knives.
Needing a serrated edge limits your choices a lot. There are a bunch of CRKT options, and the VEFF serrations are really quite good, but CRKT can be real hit or miss on quality from knife to knife and model to model.
Some of the best serrated blade options come from Spyderco, and a Byrd would be a perfect warm up to determine if a Dragonfly, Delica or Salt might work for you.
