welcome!
I'll chime in just to get things started. There are tons of solutions to your requirements. I'm not an expert on headlamps - there's a whole sub forum for that.
The requirement that limits things the most from what you said is that you want a headlamp and hand light that use the same batteries. That (mostly) limits you to either AA lights or 18650 Li-Ion lights.
Wearing an 18650 light on your head is going to be heavier, so most of those have 2 straps (one around and one over). If you don't like that then you're probably looking at AA lights. A quick browse of those recently showed me that even most AA headlamps are 2 strap as well, with the batteries in a pack in the back.
I only know two AA headlamps that have single strap. - the Fenix HL21 and Zebralights.
The Zebralights have a unique style that many people worship in headlamps- check out their website. They give tons of light for little battery, are mostly light weight and they are tough -
BUT, they are expensive and none of them project (throw) too far. They all seem built for upclose work (they have other great features as well). The Fenix HL21 is light weight, single battery, has a flip up diffuser for close work. With the diffuser up it has nice throwy beam. And, it's not expensive (~$30). The low could stand to be a little lower and it's not that tough.
AA hand lights used to be limited to small lights that didn't throw far, but these days you can get real blasters that take AA -albeit ALOT of them - so the hand lamp will be on the heavy side. You should definitely get rechargeable AAs (NiMh) and a charger. You can look at hand sized AA throwers from Eagletac, Sunwayman,Fenix, and Nitecore.
I would start from this. Figure out if you want to use AAs or 18650s, then browse (I would expect you'd be looking at single 18650 lights). If you want throw from your hand light, you want a big-ish head. If you find a light you like go to the review section and find a review - the reviews by Selfbuilt always include a comparison with all the lights that are similar so it's great way to find a bunch of lights that fit your needs very quickly.
With your budget -i'd probably go for a single 18650 headlamp (the Zebralight) and a single 18650 hand light (remember you'll need to buy 2 batteries - about $20 each, and a charger for another $20.)
For hand lights I'd consider the Armytec Viking, Eagletac G2c2, Olight M(something), Skilhunt Defier(?), but there are many more.
Hope this helps.