The bit about what you lose or do not lose on progression, I think, is going to be entirely dependent on how the "items" found in a run work.
Most games of this sort do them in pretty much the same way that Isaac does: They are what powers you up over the course of that run specifically, so that you are able to progress from the easy parts of that run, to the harder parts of that same run. Just imagine though if ANY of the stuff in that game actually carried over from one run to the next! The way that game's items work, it'd be a disaster.
Now that being said, I have a couple of ideas as to how this could work, so bear with me here...
Firstly, in the email I just sent to you, I mention a particular game as an example of certain things, but that game is also an example of this. There are things outside of your run that you unlock, sort of like in Rogue Legacy but not all grindy. But at the same time, there's ALSO the items like the ones in Isaac, which DONT carry over. So you have something that does, and something that doesnt. Rogue Legacy didn't do any of that second bit; you had what you brought with you, and that was pretty much it. And honestly, I think that created a good deal of problems with that game.
But there's a couple of other ways to do it too.
One of my favorite roguelike-ish games, and one of my favorite games of all time, Baroque (found on the PS2, Wii, and for some baffling reason iOS) has a very unique way of dealing with this. When you die in that game, you lose everything on you. Everything. BUT. There are two mechanics in place that can allow you to hold a few things over ANYWAY, yet without doing so in a way that's all sorts of broken. Method number 1 is the ability to "transfer" items back to town/base/whatever that main area coiuld be called. Basically, there were certain set points in each run (in that game, they were always on the exact same floors every time), and when you reached one, you could send exactly ONE item through it. Any item of any type that you want, you just chuck it in, and it vanishes and it sent back. Back in the town, a character there receives these, but has a limited inventory (I think it was about 20 slots in that game). Once you're dead, you start back in the town, and before you actually head to the tower to begin your run, you can stop by and talk to that guy and grab anything from him that you sent there. This allows you to plan out your next run, giving yourself a bit of a head start based on what is going on in your CURRENT run. It actually makes for a bit of a great "tough decision" sort of thing, which I find is a really, really good thing in this type of game. You can only send ONE item through per transfer point in the dungeon, so you have to choose carefully. And you can only hold so many items in that special inventory... you cant just give yourself every item ever over time, to pick from. And of course, any item that you then take from there into the dungeon, you have a chance of losing if you die.... unless you transfer it again. And of course, transferring something means you cannot use it on the rest of that particular run. I, personally, love this system; I've seen a couple of other games do something similar, but not many.
Method number 2 though is.... hmm, I"m not sure what to call it. In that game, there are these things called "brands" that you can use on basically.... anything. You stick one onto an item, and it does something, and is stuck on that item; only one brand at a time. There's a specific one that when stuck to something, causes the item to NOT vanish if you die. It isnt sent back to the town though either; instead, that item (with it's exact stats, whatever those are) is guaranteed to appear on the very first floor of the tower when you begin another run. The catch: once it does this, that brand "breaks", yet is still stuck on there. So it wont do that again, and you cant just re-brand it, you need an item to remove the effect (and that's a whole other confusing explanation). But that particular mechanic can make for a GREAT insurance policy for items you're finding to be really good at the time, and the item that actually does the branding is extremely satisfying to find. It's like a "Heck yeah! THIS thing!" sort of moment, pretty fun. It's less fun when I accidentally launch the damn thing at a monster instead of using it, but that's another story....
Also: I think RL's "progression by gold" system isnt a bad idea, but the biggest problem is that you always always always use or lose *all* of it between runs. Well, I mean, you can cause small bits of it not to be lost by a certain upgrade, but for the most part, you're resetting that amount. I think something like how currency worked in BD is better; even if half of your team is all smashed up, you're taking all that money with you and such. So you ALWAYS get a chance to do something like that between dungeons, or just hoard it if you want. I think that works really well.
Anyway, just some thoughts on that.