For starters, I'm no expert on this but from what I know, 2 'situations' arise.
1) Some Manufacturer Warranties WON'T warrant their hardwood floor systems that are installed directly over a radiant floor system in ANY scenario. This is, generally, because a heat source (radiant heat) that close to a wood surface may foster wharping and such. Wood tends to absorbe and release moisture over time. By adding such a heat source, you will accellerate wharping and aging and so on. This NOT to say that there aren't hardwood systems out there that have 'no problem' with what you want to do. You may just need to read the Installation Instructions AND the Warranty BEFORE you buy the hardwood flooring.
2) Some Manufacturers will allow you to install a radiant heat system BUT you have to follow their guidlines. In this case, as in the previous case, READ the Installation Instructions and Warranty BEFORE you buy the flooring!
Now, as for engineered vs. hardwood, I can only speak of these when it comes to NOT having a radiant floor system. (So keep this in mind ...) Engineered floors are relatively new. They're less expensive then traditional 3/4" hardwood and popular for DIYers. There are many 'construction types' among the various manufacturers. For example, you can get an engineered floor that's all SOLID woods but only the TOP-most layer is the 'good stuff' (like oak, maple, etc., etc..) There are floors where the TOP-most layer is the 'good stuff' BUT the remaining layers are softer woods. And there are floors where the TOP-most layer can be refinished 2 or 3 times (like traditional 3/4" hardwood), and there are floors where you CAN'T finish the top-most layer. (You simply throw it away when it 'wears out'.)
Here's how I approach this job. Your floors, whether it be hardwood (solid or engineered or laminated), or it be carpet, or tile, or whatever, is what folks will see first when they 'step into' your house. How it looks is VERY important. No one 'likes' (or wants) to see a 'crooked floor'. Or one that's wharped, or one that looks like it doesn't belong where it is. IMO, your flooring will most-likely affect the value of your home. Beings that hardwood floors, traditionally, add value to the home, I feel it's best left to a pro. I will tell you that unless you know what you're doing, you may end up calling that pro anyways if it doesn't turn out the way it's suppose to. In short, there are some jobs best left to a pro.
3/4" hardwood is what I like most. Yes, it costs more but not that much more than engineered floors. Remember, the will add value when you go to sell the house. WHen you walk on a 3/4" solid floor, you know it. When you walk on an engineered floor or even a laminated floor, you can hear and feel a difference. It's just 'not the same'. Also, if you choose an engineered floor, depending on the mfgr., it can be glued, stapled, or nailed. If you glue the floor down, forget about replacing a damaged strip! BUT, do ASK the Retailer about how difficult it is to replace an engineered strip that's been stapled or nailed. As for a 3/4" floor, it's, relatively, easy and not noticible at all! In BOTH cases, make sure you keep some loooong and short scraps, or order a little extra. This way, if a strip need replacement, you have the material.
I'm sure you've also seen that there are finished and unfinished products for BOTH types of flooring. I say get the PRE-finished flooring. The factory can create ideal conditions that allow many, MANY layers of finish on the strips in order to protect it. I'm sure I can say more but I'll stop for now. And I'm sure I probably generated some 'questions' with all that I've said.