You shoud proceed by sequencing purified plasmids from your positive colonies by using a primer which anneals on the vetor (not on the insert), closely to the multi-cloning-site (ie. primers M13, which should be fine for pUC19). In this way, you can control both the orientation and the identity of the sequence of your insert, to avoid SNPs owing to PCR errors.

What if I just have BamH1, Bgl1, EcoR1, Hind111, Pvu11, Sca1 and Ssp1?

You could try with a double digestion, by using different enzymes, i.e. one which cut the insert and one which cut the vector body. You have to chose your enzymes in the way that you can understand the orientation by the expected bands. However you have to be luck to have a good combination of enzymes.

I recommend to use M13 primers, and performing the sequencing of your plasmids by using such primers, only by this way you can be sure on the exact sequence of your cloned insert and on its orientation.

For M13 primer sequence give a look at here:

http://www.promega.co.uk/products/cloning-and-dna-markers/cloning-tools-and-competent-cells/puc_m13-sequencing-primers/?__utma=1.557910074.1380808193.1380808193.1395045991.2&__utmb=1.2.10.1395045991&__utm

For the map of pUC19 with the annealing site of M13 primers give a look here:

https://www.lablife.org/g?a=seqa&id=vdb_g2.3LJyH9XW3rfTWeI8E9WoB.O2B14-_sequence_467fc98be6a145d929a006d552e39e2e8e248c80_10

Good luck

As Lorenzo has already stated, automated sequencing of a purified plasmid is the better method to determine orientation of the insert. The pUC19 vector should provide good quality sequence results with M13(-21) and M13 reverse. You will really only need to sequence from one direction to confirm orientation to help save on the cost.

If your goal is only to determine orientation then one or two plasmid samples should suffice. However, if you goal is to have a plasmid with a specific orientation, you may need to do more.

Another option for determining insert orientation is to use a primer from within the insert and primers from the plasmid vector for PCR reactions. The two plasmid primers would be located to the left and right of the insert site and pointed toward it. You then just set up two PCR reactions for every plasmid to be tested. One with the internal primer and the "left" plasmid primer and a second with the internal primer and the "right" plasmid primer. One of these primer pairs should give you a product of a size that you can predict and the other primer pair should give you nothing. Since the concentration of template plasmid is so high during such a reaction, it is often possible to use primers that are not ideal for PCR, but, of course, they must be appropriately specific.

An often overlooked control for correct plasmid structure in a situation like yours is to run your plasmid DNAs on a gel without any digestion. The reason? It's possible to have two inserted segments cloned tandemly into the plasmid cloning site. If you sequence only the plasmid/insert junction sites in such a situation, you may not detect this. Running the uncut plasmid on a gel will allow you to detect any which are unexpectedly large.