Hello J.Kong, it really depends what the main consideration behind the engagement ring is. Specifically, does your fiance want a specific gemstone (may not be diamond, can be any other gemstone such as her birthday stone) or does she specifically want a diamond? Since she'll be the person wearing this engagement ring for a very long time, would be best to ask her what she likes and design the ring along with her.
If your fiance wants a diamond, then you can choose between lab-grown diamonds and natural diamonds. Honestly, the lab-grown diamonds are chemically exactly the same as natural diamonds with a far lower price. I personally cannot tell the difference between the two (full disclosure, I have a lab grown diamond engagement ring) when I was looking between natural and lab-grown diamonds. Again, it boils down to what your fiance is alright with. Is she alright with a lab-grown diamond if that means she can get a bigger carat size for your budget? Or does she 100% only want a natural diamond for whatever reason?
One thing to note is that a lab-grown diamond does not hold its value at all. It's a sunk cost, I don't think you can sell it for anything other than the gold scrap value. I believe a natural diamond can be pawned for some money to pawnshops but not a lab-grown diamond. So if resale value is important to you, then lab-grown diamond may not be suitable.
Just fyi, I got a lab grown diamond solitaire engagement ring from Michael Trio for a significantly lower price than a similarly sized/quality natural diamond ring. I'm very happy with my ring since it's just as sparkly as a natural diamond ring at a budget my fiance is comfortable with spending. Hope this helps, feel free to PM me if you have any questions about my experience with a lab-grown diamond ring vs natural diamond.