Limited budget....... I would get a folding saw (I have Silky Pocketboy) , a 4-5" fixed bladed knife, and a folder for the detailed stuff. My choice has always been the BK-15 for a general purpose woods knife, but they are discontinued and the ones I have seen still for sale tend to be priced on the higher end for this knife. So, if you prefer a Taylor Schrade product, I'd get the smaller of the two as you will be more willing to carry it. Chopping is the weak link with the SCHF36 (5"). So, I would think in terms of doing most all your major cutting with the saw, and then if you baton, slab the bigger stuff or baton smaller wood. You won't be lacking many options in the woods with this combination relative to the 7" bladed Schrade.
If chopping with a knife are really important to you, then I would look at a larger knife such as the Condor Moonshiner (9") which is fairly inexpensive, keep the saw, and carry a small folder such as a SAK. But I guess you're still in the $100 total price area for the combo. The Moonshiner is not so big that you can't do smaller tasks with it, but you won't be spreading peanut butter with it. It is a matter of style relative to your choices and willingness to carry the blades and tools.
There are many combinations that work very well and ultimately it depends on your willingness to carry them out in the woods/field and have them available for use. Hatchets are another option for modest chopping and you can certainly split wood nicely with one.