You can chosen the top ranking model in jmodeltest that is implemented in RAxML/ExaML/Fast tree. Alternatively, you can add the TVM/TIM3 models to the programs. Can't help with fasttree though. 

When you run modeltest, jModeltest or similar programs, the output can give you a feeling for which aspects of the different models are most important for your data set.  For many or most protein-coding sequences, adding an invariant class (the I in your top models) and a gamma distribution of rates (the G in your top models) makes a larger difference in the likelihood values than changing between for example a Kimura 2 parameter model and an F84 or  GTR model. 

Most phylogenetics packages (DAMBE, MEGA, BEAST, RAXML, etc) and computers today are easy enough and powerful enough that it is fairly simple to build trees using the same input data and several methods, to see if the answer is the same in all cases.  Of course there will be very minor changes in branch lengths, but very rarely will there be any substantial difference that would alter the conclusions you will draw from any tree.

With an alignment of some 80,000 bases you are surely looking at more than one gene.  It can be important to "partition" your data rather than build one tree under one model for all the data.  This would be especially true if you have put mitochondrial genes together with nuclear genes for each species in your tree, because mitochondrial DNA evolves differently than nuclear DNA. 

See for example:

Selecting optimal partitioning schemes for phylogenomic datasets.

Lanfear R, Calcott B, Kainer D, Mayer C, Stamatakis A.

BMC Evol Biol. 2014 Apr 17;14:82. doi: 10.1186/1471-2148-14-82.

PMID:  24742000

http://www.molecularevolution.org/resources/models/nucleotide

Thank you Russell John Scott Orr & Brian Thomas Foley for the response. 

@ Russell, How can we add those models to the programs?

@ Brian Thomas, 

I am not looking at more than a gene. For a single gene, I am having bases of nearly 80,000 length & more & I am not considering mitochondrial genes too.

And my doubt was, can we use any other models (e.g., TVM, TIM) other than GTR in RAxML/Fasttree? And I prefer Fasttree, as my sequence length is large. RAxML is showing memory issues, while running the data set. 

If you have a single gene of more than 80,000 bases, surely you have introns as well as exons included.  In mammals and many other organisms the introns can evolve quite differently than the exons, so again it could be useful to partition the data into protein-coding exons and non-coding regions (introns and the 5' and 3' untranslated regions of the mRNA).  But all of this depends to a large degree on how diverse your sequences are.  If they are from members of closely related species or individuals of the same species, it is a bit different than if you are comparing invertebrates to vertebrates for example. 

For very closely related sequences, the majority of the columns in your multiple sequence alignment will be invariant and thus contain no phylogenetic information even with more than 100 sequences in the alignment.  One option could be to study only the phylogenetically informative columns.  But another option is to find out how easy it is to  change memory sizes available for your programs such as RAXML.  Some programs  are built to be scalable to large computers (and have an option like "set memory_size = 40 gigabytes") and some are not.

Another thing to check for, with closely related sequences of great length, is recombination.  Within one species for example, chromosomal crossovers will occur and it is possible that this has influenced the evolution in your data set.

@ Brian,

Thank you for the reply. Yes, of course the sequences are having introns in it. Can you just brief me how to partition the data into protein coding exons and introns. Also the sequences I am considering are not that closely related. They are a little diverse group of organisms. Also could  I  know, which one do you think is the best multiple alignment tool (considering the accuracy as well as speed) ?

I don't know of an automated tool that reads for example an annotated GenBank entry saying that exons are bases 345 - 798, 12,345 - 12,596, etc (and thus bases 799 - 12,344 are an intron) and then creates the NEXUS data blocks for you.

For an example data file in NEXUS format:

http://paup.csit.fsu.edu/data/primate-mtDNA.nex

the "partitions" description looks like this:

---

begin assumptions;

charset coding = 2-457 660-896;

charset noncoding = 1 458-659 897-898;

charset 1stpos = 2-457\3 660-896\3;

charset 2ndpos = 3-457\3 661-896\3;

charset 3rdpos = 4-457\3 662-.\3;

---

Creating your partitions by hand would be a real pain to do.  

There are probably many better ways to go about solving your problem.  One would be to use a program that builds a guide tree then examines each column in your alignment to determine how it is behaving (rate of evolution etc) according to that tree, adjusts the parameters for each column, builds a better tree, and iterates that until it converges on a "best tree".

See for example:

Bayesian selection of nucleotide substitution models and their site assignments.

Wu CH, Suchard MA, Drummond AJ.

Mol Biol Evol. 2013 Mar;30(3):669-88. doi: 10.1093/molbev/mss258. Epub 2012 Dec

PMID: 23233462

Selecting optimal partitioning schemes for phylogenomic datasets

Robert Lanfear, Brett Calcott, David Kainer, Christoph Mayer and Alexandros Stamatakis

BMC Evolutionary Biology 2014, 14:82 doi:10.1186/1471-2148-14-82

http://www.biomedcentral.com/1471-2148/14/82/abstract

You should follow NCBI

I used jmodel test and it works just fine.