Blind splines will allow you to glue up the pieces while leaving the ends unaffected. Splines for the long grain side. The trick is to flatten and thickness your stock BEFORE you cut the grooves for the spline. Flatten the top either with a hand plane or a planer. Cut all the grooves with the flattened face down. This will help greatly on producing a flat glue up. Do the flattening, cut the spline, glue up and clamp on the same day. Wood can warp enough to be annoying in one day. Be very careful in selecting your stock. Quartersawn is your best bet for this kind of project.
The grain of your splines should be cross grain, the grain should run perpendicular to the long pieces' grain. This means you will have to piece together the spline piece by piece. I'd thickness the spline material and match the grooves to the spline thickness so it's a snug fit. If you don't have a planer, you can use your table saw or band saw to resaw your spline pieces to the thickness you want. Then trim off short pieces for the spline. If you use your table saw to resaw, make sure your blade is exactly 90 degrees to the table. If you don't have a Wixey digital angle gauge, get one first. They're $30 on Amazon.
If the piece you're resawing for splines is 3/4, you can get two quarter inch wide pieces from each pass, and if the material is too wide to split in one pass, you can flip it over and resaw the other half. Try not to have the blade overlap the first cut on the second pass. This will allow you to cut at least a 5 inch wide board for splines.
You can use splines to attach a finished edge to the short ends. Make a nearly full length groove, but not all the way across, in other words, a blind groove. Remember, face side down on the router table, or face up if you're cutting the groove freehand. Place 3-4 splines here and there along the groove to allow a little freedom of movement for normal expansion and contraction.
You can use pocket screws to hold the table pieces in place during glue up, but put the screws in through bottom side and use a cawl to hold the pieces firm, finished face down as you pocket screw them together. Once glue is set, you can remove the screws and even fill the holes. But you really don't need then since you're using splines for alignment, and everything cut flat face down will align pretty well.
This method will allow you to get a very flat table top that will require only a minimal amount of sanding to level. Finally, I'd consider using a scraper for a final pass to smooth out the top. Nothing looks better than the effect of a good finish on a scraper prepared table top.
Again, I'd go with quarter sawn wood for the long pieces. It costs more, but will be easier to get a great result. BTW, if your stock is 3/4 inch, your spline should be about a quarter inch thick. I love splines. Easy, strong, invisible, although a through spline with a different color between equal width glued up material can really look nice. One nice thing about a solid wood top, you can put a beautiful edge on it.
Hope this is helpful.