They'll already have solder on them from pasting the whole board.
Hot air: apply flux, hold the component in tweezers and wait for it to melt. Position gently, bump it into place -- if it doesn't snap into place with a little wiggling/bumping, apply more flux, or try to remove solder bridges. An iron should be easy enough to remove bridges with, or fine solder wick if nothing else.
Iron: position the component over the footprint, tack one pin; it'll probably be floating a bit over everything because the solder on the other pads is standing proud. Take a moment to nudge the part into alignment on the other row (moving the body, bending the one tacked pin), and tack the opposite corner. Go back and forth until it's centered and lined up. (Back-and-forth really shouldn't be necessary for a mere SOT-363, but is important for getting TSSOP, TQFP etc. in place.) Then melt a whole row at once, and press it into place. You'll need a wide/flat enough tip to do this; conical tips suck, a wedge or chamfered-cylinder style is better. You shouldn't need any added solder (again, it's on the board already), and just flux as needed to keep things clean and flowing.
FYI, I have average to good vision, so take this as-is, but I find it surprisingly easy to spot minuscule details of things -- this works because you don't necessarily need to know the exact shape of what you're looking at, just whether something's out of place, misaligned, or connected improperly. Namely: if the solder doesn't form a fillet, you won't see the shiny band around the leads; if it forms a short, you'll see extra shiny between leads. It's about the specular reflection -- which itself might manifest as a blob the size of the pad in your visual field -- but seeing where it's aligned, how it's shaped, and the relative brightness, you can still see what's going on. It may be poor resolution, but it's high contrast, too. Uh, needless to say, work in a well-lit room too!
And then, yes absolutely, use a 10x loupe or even better microscope to inspect things up close and really get to see the profile of solder joints: toe, side and even heel fillets, component alignment, etc.
Finally, test it cautiously, if you can. Bring it up slowly, or a piece at a time, so nothing powerful is likely to destroy itself. Sections you can't isolate, take extra time to inspect. The assembler won't have taken time to inspect and rework your boards, not at that budget -- this is your responsibility. Head-on-pillow, tombstone, tilted and absent parts are the most likely issues, the first one being hardest to inspect.
I take it it's probably too late to change this, but a note for the future (and if you already have, then a note for readers) -- if you're going to be doing lots of manual (iron) rework, be sure to leave ample toe fillet (sometimes side as well) to get a wedge (or even radiused) tip in there. Typically 0.3mm toe (MMC) is the minimum, and 0.5, up to 1mm for large parts, is a good idea.
Hot air is generally preferable, albeit slower (for which, a preheater helps reduce heating time). Entry-level units are cheaper than good soldering irons, there's hardly any reason to avoid having one.
You'll certainly need hot air anyway for no-lead parts, but it's also preferable for small parts (0402 say) which just wash away under the iron, whereas under hot air you just put the part in the general vicinity of both molten fluxed pads and *click* it snaps into place. (I tend to use minimal size pads for 0402, for this reason -- large pads are more prone to tombstoning).
0603 is kind of marginal between preference (hot air vs. iron), obviously they're a bit harder to see (especially with poorer vision) but they're not terrible for iron soldering. 0805 up seems to be the more suitable range for soldering iron work, and is still my default component size if I don't have any particular requirements on a project. Maybe you'd prefer 1206 if your vision isn't as sharp, or your hands are a bit shaky.
I find SMT better to hand assemble than THT, if for no other reason, it's less bother -- that's a lot of forming and trimming leads, and the soldering is slower. And there are many other reasons: lower profile, better performance, tighter layout, meaningful component choice (most stuff isn't available in DIP), etc.!
Tim