As you have mentioned, the basic Fischer operations are: Vertical positions are below the plane of paper and horizontal positions are Above the plane of paper, thus you have already remember that when working with Fischer projection. What you have to remember about chiral compounds are: If you switch two groups, you get the epimer and if you switch two other group on same chiral center, you got original compound back as demonstrated below with your compound of interest (2-bromo-1-phenylpropane):

The Cahn-Ingold-Prelog configuration of the $\ce{C}$2 is $(2S)$ while that of the epimer is $(2R)$ after first switch. You get back the original $(2S)$ configuration after the second switch. I want to do this because to get $\ce{H}$ and $\ce{Br}$ in anti-positions. The $\ce{C}$1 in the molecule is not chiral. Yet we'll do the same in case if you have to do this with a compound having two chiral centers (I'll replace one of $\ce{H}$s with a $\ce{R}$ group):

As shown, after first switch on both chiral centers, you get enantiomer (both chiral centers changed the stereochemistry). Yet, after second switch on both chiral centers should give the original compound. Make sure you change the groups as you want them to be. I put $\ce{Br}$ on the top and $\ce{H}$ on the bottom to get the best placement for the anti-situation. Yet, they are not in anti-positions since both are below the paper as shown in the second structure of the bottom line. To get into the anti-position, you must rotate the $\ce{C}$1 $180^\circ$ clockwise or anticlockwise as shown. Now $\ce{H}$ and $\ce{Br}$ in anti-positions so that the anti-elimination can occur. If that happens, the groups are in trans-positions, and the final product is Z-isomer in my case as shown. However there were two hydrogen in the $\ce{C}$1 in your case, and hence, more stable E-isomer would be the major product. Still, it would give you small amount of Z-isomer as minor product (you may see gauche-interaction between methyl and phenyl group in the anti-II conformer).
Note: If you know how to convert Fischer projections to Newman projections, it is easy to visualize and you may able to see why is the major product to be E-isomer.