Cut Reliably
I really just need it to cut reliably but not be so flimsy that it will break.
Just off the top of my head . . . the Becker line (hso's suggestion), the ESEE line, and perhaps something from Ontario, are generally accepted as "heavy use" knives.
If you're already gonna have a saw and axe, then we could dispense with the "heavy duty" aspect and focus on decent quality and cutting.
In that department we have brands like Buck Knives (the 105 stands out as a practical size, the 119 is perhaps a little large), Mora -- which covers a wide range of prices, like from $12 to $150 -- which are legendary in the price-for-performance category. See
Ragnar's Forge for a good survey of those, and (also on Ragnar's Forge) knives from Finland (e.g. Marttiini and Järvenpää) and Norway (Helle, Brusletto).
Buck also has a fairly broad range of styles if the traditional 102/105/119 styling is not to your liking (the
Vanguard, for example, or the newer Buck/Hood
Punk).
I'm making an assumption that you will always have a general purpose folding knife on your person in addition to whatever is in the bag. If that's not true, then it's perhaps wise to add a decent medium-to-heavy duty folder to the bag as well. There are a whole bunch of those out there: Spyderco, Buck, Benchmade, CRKT, Kershaw, and so on. But for now, I'm going to assume that, since you have your pants on, you also have a folding knife with you.
If I were shopping for an inexpensive but reliable fixed blade knife, my first choices would be Mora and Marttiini, with Mora a slight favorite. Most of these are under $50. I have a Mora #1 that I picked up in 1973 or 1974. Still sharp. Still strong. It could probably use a new handle.
If I have a little more cash, and I can afford something in the $50-to-$100 range, I might look at the Ontario/Randall or ESEE knives, maybe a Becker Campanion or Magnum.
Something to keep in mind, though, is that your general purpose "survival" blade should be light enough and versatile enough for camp kitchen use, game dressing and skinning, in addition to the usual "woodcraft" stuff. Depending on your hand size, hand strength, dexterity, and stuff like that, you may find a large blade awkward for certain common tasks. If that's the case, you might consider two of the more inexpensive knives in different sizes.
Regardless of which fixed blade you choose, you should also add a durable multi-tool as suggested above. Leatherman, Gerber, SOG, or something like that. 'Cuz you just never know.
My own personal choices for "survival" knives look kinda like the following, provided as suggestions for your consideration:
Mora 2000, $30, lightweight, ergonomic, durable, sharp as the dickens.
Ragnar's Forge.
Mora Craftline, $14, light & good ergos, durable, shaving sharp.
Ragnar's Forge.
Marttiini knives of this essential style, around $25, light/ergo/durable/sharp.
Smoky Mountain Knife Works.
Järvenpää Puukko & Leuku combo (mine's in stainless), Sammi/Lapp traditional.
Ragweed Forge.
Buck 105
Pathfinder. Light, sharp, strong. Good general purpose cutter.
Most sporting goods stores; also direct from Buck Knives.
Buck 102
Woodsman. Light, sharp, strong, small, versatile.
Most sports stores; also direct from Buck knives.
It's a small knife, but it will do deer, fish, camp work, and kitchen work.
I also have a selection of medium-to-heavy folders on hand. Here's a photo spread of
some of them. Left-to-right: Buck 110, Buck Vantage, EKA (Normark) Swede 92, Case Sod Buster (large), and Benchmade Steigerwaldt 12700.
Others, farther down the spread, are the EKA Swede 88 (light birch handle), and the EKA Nordic T8 (dark bubinga wood handle).
Things to avoid: in general, avoid knives branded after major firearms manufacturers. Some are good. Many are not. Most of the good stuff out there isn't gun-maker-branded. Time enough to sort through all those later.
I generally recommend against knives with serrations (combo edges). It's a personal thing, and you might learn that you prefer them. I find them troublesome.
At this time I have trouble recommending Gerber as a brand. I own some of their earlier (1970s, early '80s) pieces, and they're excellent. I haven't been able to find any of their newer stuff that measures up to that earlier standard. I do have a couple of modern Gerber pieces with which I'm happy (e.g. a Harsey Hunter), but mostly I haven't achieved a good level of confidence with today's Gerber products.
What I've offered above is not a comprehensive review of what's available, and tends to be limited to my own experience.
Don't let that put you off trying other stuff.