I agree with most that has already been said. But one question comes to mind (that I haven't seen asked yet. Is your sawmill a chainsaw mill e.g., Alaska type? If so, you will need a good ripping chain.
If you are just bucking up into the length you want, I honestly don't understand why you would want anything bigger. A 26" bandsaw mill will, with quite a bit of effort (do you hear a chainsaw buzzing in the background for the off round bits of the log?), saw up a 25-26" Dia log with typical "lumber width" (or between guide width) of 20-22" (which means you cut a full 2" - or more - off each of the 4 sides). Also, when you start felling 26" trunks, be aware you will probably be looking at sharpening after every other cut or every 3rd cut (sorry, I'm old school and my experiences with carbide tipped chains have not been that great - think running into metal while felling/bucking, bye bye $200). Be aware that if you Don't have good curls from the cut wood coming out of the saw e.g., like chips coming out of a planer, NOT large sawdust, your blade is dull (dangerous) and is working much harder than it should be - maybe this is why you believe your current saw won't work for you.
I know many, many folk that "think" if the chain is still going around on the saw its fine and should only be sharpened once or twice a year.
The saw you have is more than enough to work on pines and probably enough to work on most native hardwoods - exceptions would be ultra hards like ironwood. Again though, only if you keep the chain sharp.
If, as you state, you are a newbie feller, please consider finding an experienced professional timberman (not just a tree trimmer), and see if they can help you out on technique - most will be happy to help out if they are any good. The advantage to this is that they will have local knowledge of the trees and things to watch out for.
As far as equipment, at the bare minimum let me suggest a few items. First, if you are planning on a full day's worth of felling/ bucking, consider buying several chains (I take 5 with me for hardwood work). With several chains you can make sure they are all sharp so you can change out in a few minutes, rather than losing momentum by stopping to take 20-45mins, or longer, to sharpen the attached chain.
Second, if you haven't already purchased felling wedges (plastic only!), buy at least 6. If you can find different widths, all the better. If you don't know what I'm talking about, ask the professional timberman. Finally, DO NOT skimp on safety gear, ear, eye & leg protection!
Oh, BTW, if you've never used a bandsaw blade sawmill (or any sawmill for that matter) that isn't hydraulic assist be sure to eat your Wheaties, you'll need it. Sawyers don't have large biceps, etc because they go to the gym!
Hope this helps!