An inexpensive scrapper build?

Taking into account I16, any choice on power sets that don't break the bank?

Any/any. That's not a ******** answer, seriously.

Now, if you have a specific goal in mind (AV soloing without insps/temps, +4/x8 missions, PVP) you'd want to state it to have detailed answers, in my opinion.

With Fire/SR you can soft cap your defenses and get a good attack chain for relatively cheap. You'll still need an IO set build, but it's doable on the cheap if you bid patiently.

I'd guess about 300m ish

Claws/WP, BS/WP, DM/WP or Kat/WP are good out the box and still very survivable in end game content with a purely SO build. Personally, playing those combos is easy mode.

Looking for something that requires a little (lot) more strategy? Try those sets with /regen. Also good out the box and still good in the end game with just SOs. That is if you know what you are doing.

Would DM/Electric work without getting into expensive IO sets?

I find it easier to make a giant pile of inf than worry about what my IO's are going to cost.

It isn't hard, hit the link in my sig if you want more info.