OK - I am confused - maybe a terminology confusion.
A septic pump (commonly called a sewage grinder lift pump or lift station pump) is used to lift sewage from a low point to a higher elevation to discharge to a higher level waste pipe. Normally used only in public sewage systems as they are VERY high maintenance. However, if you have a situation such as full-basement house with basement bathroom located in level terrain so you have to lift up to the septic tank or sewer pipe, or a septic tank and leach field higher than the basement, maybe you do need one. I doubt this is your case, as you obviously do not have one now. Ballpark estimate, about $1000-1600 for a decent pump and sump, plus $1000-2500 install including digging for pit, depending on length of piping and electrical runs needed. I would emphatically recommend a pedestal type rather than submersible, as it will generally last a lot longer and is a lot less messy to work on, as well as generally being cheaper. Be sure to get one with multi-story line powered plus battery backup alarm system, so if it fails an alarm goes off to warn you not only downstairs but upstairs as well. I would NOT go with a $200-300 box store special - you want a commercially rated unit for any kind of reliability. I would also go with an oversize pit with a fairly low fluid level setting on the overflow alarm (NOT full), so if the pump fails the high level alarm will sound but the pit will still have capacity to handle a couple of more flushings.
I would also consider, depending on your situation, seriously talking to the plumber about a split system, which many areas require by code. This means running all the main house sewage direct to the sewer to the extent possible, with only the basement running off a lift pump, if your topography and pipe elevations allow for that. That greatly reduces the load on the pump, leaves you with working bathrooms upstairs if the pump fails, and eliminates the shower/tub/clothes washer overfill problem if the pump fails, as the pit will rarely have enough capacity for the amount of water they put out (10-50 gallons per use).
Also have the plumber inform you of minimum use cycles - you need to flush or run water every week or less to keep the pump clean and in good condition - if it just sits unused it will grunge and solidify up and fail.
I would emphatically recommend a pedestal rather than submersible type pump - last way longer, and easier to maintain because the motor is not submerged - only the pump head. Talk to your plumber about grinder versus waste transfer pumps - the latter are about half the cost but cannot grind up any plastic, wood, rags, etc, so plug up more easily if anything other than human waste get into them - I would go for the grinder type for any installation, myself, jsut for peace of mind and not having to manually clean it out periodically because it plugged up.
And of course, be sure the plumber briefs you on how easy they clog and how to unclog it, and put up a sign in every bathroom and powder room about not putting ANYTHING foreign in the toilet - otherwise when you have guests over, expect trouble. Also make sure your kids brief their friends when they first come over - they will probably think this is gross sounding, but better to enforce the rule and make sure they understand the consequences if the pump gets blocked.
Second possibility - that you actually mean a SUMP PUMP. This is a pump that lowers the water table locally under your basement, to eliminate wet or weeping basement slab issues, but does not handle sewage.
Depends a lot on how much water you are talking about, and where entering basement. Basic sump pump installation WITHOUT lateral drains or drain tiles about $150-300 to do it yourself, $1000-2000 by a plumber. National average seems to be about $1000, based on a quick search. I would emphatically recommend a pedestal rather than submersible type pump - last way longer, and easier to maintain because the motor is not submerged - only the pump head.
Battery powered backups for the pump are also available in event of power outages - is basically a battery-operated pump in parallel (independant of the main pump except uses same drain pipe) - about $500 more plus probably $100-200 install if done at same time as main pump. Be sure comes with alarm system for high water, low battery, battery charger failure, etc.