Okay - I hope you understand the "spot weld" idea...
You're going to want to drill holes in the NEW floor if you're going to lay it over the edge of the old... and then you'd do a "rosette" weld thru the hole you drilled -- filling it -- and it will "look like" a spot weld...
You could "reverse" this if the overlap would be the other way around... then you'd want to lay your new stuff up there and mark where you're going to weld - and clean that little area down to bare metal.
OR -- you can butt weld the new floor in -- and this will take a lot more prep work - but gives the final product a "never been worked on" finish if that's what you're going for. If this is the case - FIT UP is paramount to good welding to follow.. you want really tight gaps that are consistent (1/16") and to do that you're going to need some extra tools - lots of clamps - cut off wheels and grinders and tin snips etc in order to SCRIBE the old onto the new and then be able to sneak up on the fit (to get the gaps right). Then you'd have that all clamped in and fitting right - and you'd tack it in - and then go back and finish weld it - by skipping around - weld an inch here - move to the other side weld an inch etc... until you had welded it all the way around. THEN you'd use seam sealer and you could metal finish the underside so you'd never know it was done.
None of this is rocket science --- but does take some time - and lots of patience to make it look and fit right. CLAMPING either way is critical -- you've got to use lots of clamps when you're welding. Metal expands and contracts when you're welding on it - and you don't want to be warping stuff. And CLEAN metal is important to making a good weld. Welding on rusted or painted areas is a total no no. Be careful to not grind the metal -- just get it clean - it's thin enough already!

Don't make it more work than it already is... but grinding what little is there down to nothin'. When you're tacking -- cut your stick out at an angle EACH tack... that will help you with burn through. The tiny "tip" of the fill wire will start the weld quicker with less heat and get you a nice tach. Wire is cheap and you're not "wasting it" by doing this - try it and you'll see what I'm talking about. CLEAN metal - and sharp "stick out" with good fit up and you'll make nice tacks.
Welding this stuff is like painting -- good PREP is key to good paint. It goes for welding too. The welding is EASY if you've done your prep right. It's hard and a lot of work when you're burning through and have a nasty ass looking job when you're done.
So if it was me -- I'd prep all my "old" edges first - using a wire wheel - or some 3M Roloc discs... etc. cleaning them top and bottom to bare metal... back at least an inch. Then I'd see where the new has to go and what I have to do to prep it.