With those cast furniture parts I approach the filing with a light hand at first. What I want to do is find out where the pits and minor casting flaws are under that bead blasted finish before using a heaver hand to get below them. Try and not add to the pitting and such by scoring the metal with your files, this means keeping the files clean as you work. This is especially so when draw filing a barrel. Emery paper (auto store) is what you want when it gets down to the "sandpaper" part, but there is filing to do beforehand. Regular sandpaper isn't much use until you've arrived at the finishing grits. For browning I take it to 240 or 320. You want to remove all signs of the previous grit before moving to the next higher one, this means using cross-hatching strokes as you go. It is a lot of work.
I like the LMF browning solution quite a bit, it is very forgiving and results in a very nice brown. I've no experience with the plumb brown, can't advice you there - rsells remarks were right on though. With the LMF the first two coats might look a bit streaky and uneven, with coppery spots, don't freak out - all that will even out as you apply more coats. Don't rush the process either, here in the south where we live in a natural browning box I might get one of two coats a day on the metal. If you apply it too often you run the risk of the rust building too fast and flaking off. I card using a rough square of canvas or tow sack material, do it, card, before applying the next coat. Get all the red/orange rust off everywhere, the apply more. Generally it takes six or seven coatings to obtain a nice even brown.
When applying the LMF do so with a light touch, almost no pressure. All you are doing is wetting the surface with the solution. I use small squares of cotton cloth, cotton balls and Q-tips.
Good luck, it isn't as difficult as it may seem, I believe you'll have good results with the LMF.
dave