Hints on making a model
To make a model, you will need a sturdy cardboard box that is closed on five sides, strong thread cut into pieces about six inches longer than the height of the box and a strong needle with a large eye (that can be used with the thread),  forty beads, and paste or glue. Measure the small dimension of the box. This will correspond to 16 light years and will give you the scale for your model.

Turn the box so that the open side faces you. On the center of the top, draw a small circle with a dot. This will be for the sun. It is on the first line of the table you have looked at. Tie a knot at the end of one piece of thread and thread the needle with the other end. Insert the needle and thread through the box on the dot. Thread a bead on the needle and fasten it so that it is in the center of the box. (You can tie another knot to hold it or use paste or glue.)
Glue the other end of the thread to the bottom of the box so that the thread is vertical. (You can either glue it inside the box or thread it through to the outside and glue it there.)

Compute the X, Y, and Z coordinates of each of the other stars.
    X = 3260 * cos(RA) * cos(DE) /plx
    Y = 3260 * sin(RA) * cos(DE) /plx
    Z = 3260 * sin(DE) /plx
(* is a sign used for multiplication with computers to keep from confusing the multiplication symbol with the variable "X". Sin and cos are trigonometric functions. If you are not familiar with these, have your teacher help you. They are probably in the calculator on your computer if you request the scientific view. It will be even easier to use a spread sheet. )
To determine the sin and cos on the computer, you will have to change RA and DE into degrees and, possibly into radians. This is done as follows:
    RA in degrees = 15*(h +min/60 + s/3600)
    DE in degrees = deg + arcmin/60    if deg is positive
    DE in degrees = deg - arcmin/60    if deg is negative
        (Be sure to keep the sign with DE)
To change from degrees to radians, divide by 57.3.
If your teacher agrees, you can use a table in which the the position in radians and X, Y, and Z  have already been calculated. This table also contains the tangential motion in km/sec.

Now, on the top of the box, plot the position projected on the galactic plane of the earth's equator of another star. You will note that in some cases there are two stars at the same position. These are double stars. Use a single bead but you may want to mark these in some way to indicate that there are really two stars. Thread the needle and insert it into the box as you did for the sun. Fasten a bead at the correct Z coordinate for that star with positive Z higher than the sun and negative Z lower. (Use the sun as the zero point and the scale you determined above.) Fasten the other end of the string as you did for the sun. Repeat this procedure until each star within 15 light years of the sun has been correctly positioned.

You may want to use beads of different sizes with the absolute brightest star the largest and the absolute faintest, the smallest. You will need more small beads than large ones. You might also want to use beads of different colors as follows: for B-V<0.3, use blue beads; for 0.3<B-V<0.8, use yellow beads; for B-V>0.8, use red beads. This will give you an idea of the sizes and colors of the stars near the sun. If possible, check you table to see how many of each size and color you will need if you wish to do this.

If making the model is too time consuming, you can get some idea of the distribution of the stars by plotting their X and Y coordinates with respect to the sun. You can make the size of the dots correspond to the absolute brightness of the star and use colored pencils to indicate the color of the star. Since you will not need the Z coordinate, you may want to use the RA directly with the hours and minutes placed as they would be on a clock (using the hour hand only). This gives the angle from the sun. The distance is (3.26/plx) * cos(DE).

Notes on Star Colors
Your diagram shows that most of the stars lie along a smooth curve with the redder stars fainter. These stars are called "main sequence" stars. They shine because they are converting hydrogen to helium in their cores - the longest portion of the life of a star. The bright, blue stars use their hydrogen quickly and do not live as long as the faint, red ones. That is one reason there are fewer bright blue stars. Also, these stars are very massive and there are few massive stars than smaller stars born. The few stars that are both faint and blue are called "white dwarfs". They are stars that have used all of the hydrogen that can be converted to helium. They are slowly collapsing with the gravitational energy changing to thermal energy heating the stars. Eventually, when they can no longer collapse further, they will cool into dead stars.
How to determine which star will come nearest to the sun
This is easy if you know trigonometry but can also be determined graphically. First make a velocity triangle for any star that is approaching the earth. Draw an arrow pointing to the sun whose length is a scaled radial velocity. Perpendicular to the tip of this arrow, draw an arrow whose length represents the tangential motion to the same scale. Connect the start of the radial velocity arrow (the star position) with the tip of the tangential velocity arrow. This line is the direction of motion of the star. From this triangle, you can see that the star that will come closest to the sun is the star for which the negative radial velocity divided by the tangential velocity is largest.

To get the distance of closest approach, draw the velocity triangle for the star you have selected as having the closest approach. Plot the sun at a convenient distance from the star position. (Use convenient scales for both distance and velocities.) Extend the total velocity arrow until it passes the sun. Draw a line from the sun perpendicular to the velocity arrow. The two lines meet at the point of closest approach. From the length of the two perpendicular lines (to the same scale as the star-sun distance), measure the distance of closest approach (short line) and the distance the star must travel from its present position to this point of closest approach (long line).

To determine when the star will be closest to the sun, calculate how long it will take the star to reach the point of closest approach.