You should be fine. If you read a book or two beforehand, there is no need for guides at the major sites, pyramid fields and Egyptian Museum included. I’m sure they can make life easier but not enough to stretch a budget that can be better spent elsewhere.
Your chief problem will be the touts and hustlers on the streets and at the sites. Their little tricks and scams are colourful, varied and deceptive. The usual suspects can also be persistent to the point of distraction. Having a guide can minimise but not eliminate all of this and the wrong guide can as bad or worse. Cynicism should see you through but if want more information, spend a little time combing through previous posts here and on the Luxor Forum where you should find all the detail you need to deal with anything that comes your way.
With bargaining, you can hire an unmetered taxi for a day’s touring in and around Cairo for $20 to $30 a day. (A metered driver may offer to switch it off and negotiate a flat fare.) There will probably be loads of taxis hanging around your hotel. The drivers are streetwise and sharp but when the bargaining is over, can be easygoing and helpful. If you want the best price, negotiate away from the hotel so that the driver doesn’t have to pay a commission.
In Luxor, a cab hired for a day’s touring from the east bank to the west bank should cost say LE 100 to LE 150 maximum. If you cross the Nile by private motorboat (LE 5 for the boat, not pp) or by the national ferry (LE 1 pp each way), you can hire a day’s taxi for say LE 50–60.
With any taxi you take in Egypt, always agree the fare, currency and number of passengers beforehand. The prices quoted are ballpark and you may not wish to take the time and trouble hammering the driver for every last penny but you don’t want to go over the odds either. Sooner or later, the driver will probably try and a steer you into a shop where he can earn a commission on what you buy. If you don’t want to shop, say so but, if you decide to go in (and the shopkeepers can get in-your-face persistent), ignore the sales pitches and/or hard luck stories and remember there is no obligation to buy anything.