The most important thing in a pool cue is the tip. As Bob Byrne said, give a good pool player a broom handle with a good tip on it, and he’ll run a rack on you and then sweep the joint out after.
For a home table, find some good quality one-piece cues. One piece cues are superior to two-piece cues because the joint is a weak spot in a cue. Since you’re not traveling with the cue, there’s no need to break it down.
The weight of the cue isn’t that relevant at this stage, nor is the balance. What you care about is that the shaft of the cue is straight, and that it’s the right size for the kind of pool you’re playing. For 8-ball and 9-ball, you want a tip that’s 12 or 13 mm in diameter. For snooker, you want a smaller tip diameter.
The size of the cue depends on two things - the size of the player, and the size of the room. A lot of home pool tables are in rooms that are too small. In which case you’ll want to buy a short cue for using where you can’t use a good stroke with a full sized cue.
The cue should be such a length that if you bend over and line up on the ball, your cueing arm should be perpendicular to the floor when it’s centered in a comfortable place on the butt of the cue. If you’ve got kids who are still a little smaller, make sure you get cues sized for them, as they’ll have trouble with longer cues.
The shaft of the cue comes in two types of taper - a constant taper from the middle of the cue to the tip, or a ‘professional’ taper which tapers down until it’s about 13-18" from the tip of the cue, then maintains a constant diameter from there. Snooker cues generally have a constant taper, and pool cues have a ‘professional’ taper. The reason for this is that if you use a ‘closed’ bridge which is required to put heavy english on the cueball, your fingers will be pushed open and closed with a constant taper shaft as you move the cue back and forth. Snooker players generally use an ‘open’ bridge in which they rest the cue in the ‘v’ of their fingers, so the constant taper doesn’t matter.
Having said all this, there should be no reason to spend more than $50 on a good pool cue. A $1000 cue will be prettier, but won’t play any better.
If you can find a Dufferin store in your area, they make an excellent one-piece cue for under $50. And if you do want a two-piece cue for going out to the billiard hall, the dufferin ‘sneaky pete’ is available for $50-$70, and will play as well as any cue on the market at any price. Another advantage is that when it’s screwed together, it looks like a typical ‘house’ cue, so you don’t have to be embarrassed about having a flashy cue while you’re learning to play.
If $50 per cue is too high, you might want to check out Valley cues. They’re a lower-end cue that you can find for $25/30.
You want a good leather tip on the cue. Do NOT buy a cue that has a plastic tip/ferrule that slides over the top of the shaft, or one that uses screw-in tips. These are junk. You want a shaft that has the ferrule (the white part of the tip) glued on, and a leather tip glued on top of the ferrule. That way, when your tip wears out you can just cut it off with an x-acto knife and glue a new one on.
Tips come in different hardnesses. Good tip brands include Triangle, Elkmaster, Le Pro, and Chandivert. I prefer Elkmasters or Le Pro tips. Some of these tips are very hard, some are softer. A hard tip will hold its shape longer, but won’t hold chalk as well, and has to be kept ‘dressed’ with a rasp or a tip tool to keep the surface rough enough to hold chalk.
Prepare your tip properly. This is more important than anything else on the cue. The tip should be rounded to about the diameter of a dime when held against the side of the tip. Use a file or a rasp to do this.
When you say you bought a ‘lower end’ pool table, what do you mean? Do you mean an inexpensive 4 x 8 slate table, or do you mean one of those small, non-slate tables for under $500? If the latter, you may be disappointed and decide you don’t like the game simply because the table doesn’t play well enough to really learn the game properly. if that’s the case, I recommend taking the family out to a family friendly pool hall a few times to see what it’s like to play on a quality table, before deciding that pool isn’t for you.
Hope this helps.