Lucille-if you are willing to spend several days, producing a good poly finish it is quite easy. Mix gloss polyurethane 50/50 with mineral spirits and wipe it on. It will be very thin and the first coats will absorb into the wood quite a bit. Allow to dry and then re-apply. After 5 or 6 coats, very, very lightly sand the finish with fine grit sandpaper or steel wool. Vacuum and tack rag the furniture and then apply another 5 to 6 coats of the mixture. Again sand. If you're happy with a gloss finish, apply 2 more coats of the mixture and you're done. Otherwise, mix some semi-gloss or matte polyurethane with mineral spirits in the same 50/50 ratio. Apply the last 2 coats. Because the mixture thin, you will not have trouble with runs or brush marks. Also, the dry time between coats is quite short, so you can apply saveral coats per day, if you're feeling dedicated.
If you feel inclined to try this and have any questions, please feel free to ask. I've used this approach for several years and it always works well.
Q